Collective excitations of hard-core Bosons at half filling on square and triangular lattice
Quantum Mechanics
Quantum MechanicsQuantum mechanics is a branch of physics that deals with the behavior of matter and energy at a microscopic level. It is a fundamental theory that explains how the universe works at its most basic level. Quantum mechanics is a complex and fascinating field that has revolutionized our understanding of the universe. In this essay, I will explore the basics of quantum mechanics, its implications, and the challenges it presents.At the heart of quantum mechanics is the concept of the wave-particle duality. This means that particles, such as electrons and photons, can behave as both waves and particles. This is a fundamental departure from classical physics, which assumes that particles are always particles and waves are always waves. The wave-particle duality is a key aspect of quantum mechanics and is essential to understanding its many applications.One of the most famous applications of quantum mechanics is in the field of quantum computing. Quantum computers use the properties of quantum mechanics to perform calculations that are impossible for classical computers. This is because quantum computers can perform multiple calculations simultaneously, whereas classical computers can only perform one calculation at a time. Quantum computers have the potential to revolutionize fields such as cryptography, drug discovery, and artificial intelligence.Another important aspect of quantum mechanics is quantum entanglement. This is a phenomenon where two particles become entangled and share a quantum state. When this happens, any change to one particle will instantly affect the other particle, no matter how far apart they are. This has important implications for the field of quantum communication, where information can be transmitted using entangled particles. Quantum entanglement also has implications for the nature of reality, as it challenges our classical understanding of causality and locality.Despite its many applications, quantum mechanics presents many challenges. One of the biggest challenges is the measurement problem. In quantum mechanics, particles exist in a state of superposition, where they can exist in multiple states simultaneously. However, when a measurement is taken, the particle collapses into a single state. This presents a paradox, as it is unclear whatcauses the collapse of the wave function. This has led to many interpretations of quantum mechanics, such as the Copenhagen interpretation, the many-worlds interpretation, and the pilot wave theory.Another challenge presented by quantum mechanics is the problem of decoherence. Decoherence is the process by which a quantum system interacts with its environment, causing it to lose its quantum properties. This makes it difficult to maintain a quantum state for any length of time, which is a major obstacle for the development of practical quantum technologies.In conclusion, quantum mechanics is a fascinating and complex field that has revolutionized our understanding of the universe. It is a fundamental theory that has many applications, from quantum computing to quantum communication. However,it also presents many challenges, such as the measurement problem and the problem of decoherence. Despite these challenges, quantum mechanics is a field that is constantly evolving, and it will continue to shape our understanding of the universe for many years to come.。
我想成为一名宇航员八上英语作文
我想成为一名宇航员八上英语作文I Want to Become an AstronautHave you ever looked up at the night sky and marveled at the twinkling stars and the bright moon? I sure have, and it never ceases to fill me with wonder and amazement. The mysteries of space have captivated me for as long as I can remember. The thought of exploring the great unknown and unraveling the secrets of the universe thrills me to my core. That's why I dream of becoming an astronaut one day.Ever since I was a little kid, I've been fascinated by space. I can vividly recall lying on the grass in my backyard, gazing intently at the star-speckled sky, and letting my imagination run wild. What kind of worlds could those distant stars have orbiting around them? Could some of them possibly harbor alien life forms? The very idea of intelligent beings existing on other planets both excited and intrigued me.My fascination only grew stronger as I got older and started learning more about space in school. I was in awe when I first saw pictures of faraway galaxies, star clusters, and nebulae. The sheer scale of the universe is mind-boggling, and the thought that we humans have only scratched the surface in ourexploration of it fueled my desire to be a part of those brave endeavors.Of course, becoming an astronaut is no easy feat. It requires years of rigorous training, both mentally and physically. You need to be incredibly knowledgeable in fields like physics, astronomy, and engineering. You also need to be in peak physical condition to withstand the extreme forces involved in space travel. And perhaps most importantly, you need to have an unwavering courage and determination to face the many risks and challenges that come with venturing into the great unknown.However, I am fully prepared to dedicate myself to this path. I've always been a diligent and hardworking student, especially in subjects like math and science. I'm also physically active and take good care of my health. But beyond that, I possess an insatiable curiosity and a hunger for knowledge that I believe will serve me well in a career as an astronaut.Just imagine the thrill of being launched into space aboard a powerful rocket, leaving the Earth's atmosphere behind and entering the vast expanse of the cosmos. The view of our beautiful planet suspended in the inky blackness of space must be a breathtaking sight to behold. And then, to actually set footon another celestial body, like the Moon or Mars – what an incredible accomplishment that would be!As an astronaut, I would have the opportunity to conduct cutting-edge scientific research that could potentially lead to groundbreaking discoveries about the origins of our universe, the nature of black holes, or even the existence of extraterrestrial life. The knowledge and insights we could gain from space exploration are virtually limitless, and I would be proud to contribute to humanity's quest for understanding.Of course, being an astronaut also comes with its fair share of risks and dangers. The perils of space travel arewell-documented, from the potential for equipment malfunctions and life-support system failures to the ever-present threat of cosmic radiation and the harsh conditions of extraterrestrial environments. It's a profession that demands nerves of steel and an unwavering commitment to the mission.But I truly believe that the rewards of space exploration far outweigh the risks. The knowledge and discoveries we stand to gain could revolutionize our understanding of the universe and potentially even secure the long-term survival of our species by enabling us to establish settlements on other planets.Imagine being one of the first humans to set foot on Mars and pave the way for future colonization efforts. Or perhaps even venturing beyond our solar system aboard an advanced spacecraft, exploring distant star systems and making first contact with alien civilizations. These may seem like far-fetched notions now, but with the tireless efforts of brilliant minds and the continued advancement of space technology, who knows what amazing feats we might achieve in the future?That's why I dream of becoming an astronaut – to be a part of that grand adventure, to push the boundaries of human knowledge and exploration, and to contribute to our species' quest to unlock the secrets of the cosmos. It's a lofty ambition, to be sure, but one that I am fully committed to pursuing with every ounce of my passion, determination, and hard work.So the next time you gaze up at the night sky and marvel at the twinkling stars, remember that there's a whole universe out there waiting to be explored. And if you catch a glimpse of a shooting star, make a wish for me – that one day, I might have the incredible honor and privilege of being among those brave souls who venture forth into the great unknown, propelling humanity's journey of cosmic exploration to new and uncharted frontiers.。
Edexcel GCE Physics Advanced Subsidiary Unit 1 物理
Turn over P43321A©2013 Pearson Education Ltd.1/1/1/1/C2*P43321A0132*Instructions•Use black ink or ball-point pen.•Fill in the boxes at the top of this page with your name,centre number and candidate number.•Answer all questions.•Answer the questions in the spaces provided– there may be more space than you need.Information•The total mark for this paper is 80.•The marks for each question are shown in brackets– use this as a guide as to how much time to spend on each question.•Questions labelled with an asterisk (*) are ones where the quality of yourwritten communication will be assessed– you should take particular care with your spelling, punctuation and grammar, aswell as the clarity of expression, on these questions.•The list of data, formulae and relationships is printed at the end of this booklet.•Candidates may use a scientific calculator.Advice•Read each question carefully before you start to answer it.•Keep an eye on the time.•Try to answer every question.•Check your answers if you have time at the end.2*P43321A0232*BLANK PAGE3*P43321A0332*Turn over4*P43321A0432*5*P43321A0532*Turn over6*P43321A0632*7*P43321A0732*Turn over8*P43321A0832*9*P43321A0932*Turn over10*P43321A01032*Explain the meaning of the terms hard, stiff and high tensile strength.............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................*(b) It is important that a piano wire has a high elastic limit.Explain why this is important.(3) .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. ..................................................................................................................................................................................................................................................(total for Question 12 = 6 marks)The strip of paper is shown below. The start and the end of the journey are indicated.Using measurements from the tape show that the final velocity of the trolley is.................................................................................................................................................................................................................................................. ..................................................................................................................................................................................................................................................(ii) Hence calculate the average acceleration of the trolley.(2) .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. ..................................................................................................................................................................................................................................................Average acceleration = ..................................................................(b) Using a ticker tape timer is one method of measuring the speed of a moving object ina laboratory. Another method is to use a light gate with a data logger and computer.Suggest an advantage of using the light gate method rather than using a ticker tapetimer.(1) .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. ..................................................................................................................................................................................................................................................(total for Question 13 = 5 marks)14 The picture shows a track for racing toy electric cars. A guide pin fits in a groove in thetrack to keep the car on the track. A small electric motor in the car is controlled, with ahand-controller, via contacts in the track.A child places a car of mass 95 g on the track. She adjusts the controller to a power of4.2 W so the car accelerates from rest for 0.40 s.(a) (i) Show that the energy transferred by the motor in 0.40 s is about 2 J.(2) .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. ..................................................................................................................................................................................................................................................(ii) Calculate the speed of the car at 0.40 s.(2) .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. ..................................................................................................................................................................................................................................................Speed = ........................................................(iii) Suggest why the actual speed of the car is less than the calculated speed.(1) .................................................................................................................................................................................................................................................. ..................................................................................................................................................................................................................................................(b) At high speed the guide pin may become disengaged from the groove.Use Newton’s first law to explain why the car would then leave the track at a corner.(2) .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. ..................................................................................................................................................................................................................................................(total for Question 14 = 7 marks)(b) (i) Use Stoke’s law to show that the SI unit of viscosity is Pa s.(2) .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. ..................................................................................................................................................................................................................................................(ii) A small sphere is dropped into a large volume of ethanol at 24 °C.Show that, if the drag were due to viscous forces alone, the terminal velocitywould be about 4 ms–1.Assume that upthrust is negligible.radius of sphere = 5.0 × 10−4 mroom temperature = 24 °Cmass of sphere = 4.0 × 10−6 kg(3) .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. ..................................................................................................................................................................................................................................................*(c) Diesel is used as the fuel in some vehicles. Diesel is not renewable, so alternatives are being researched. Biodiesel is a fuel made from vegetable oil; biodiesel on its own is not suitable for use in vehicles.The table gives some information about diesel, biodiesel and ethanol.Viscosity / mPa sat 0 °c Viscosity / mPa sat 40 °cEnergy /MJ kg–1Freezingpoint / °cDiesel 4.9 2.643 –30Biodiesel17.3 4.639 –12Ethanol 1.80.927–114Blends of biodiesel with ethanol are being researched as a renewable alternative todiesel fuels for use in vehicles all year round.Using the information in the table, suggest why these blends are being researched.(3) .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. ..................................................................................................................................................................................................................................................(total for Question 15 = 10 marks)BLANK PAGE16 The photograph shows an athlete performing a long jump.At take-off his horizontal speed is 8.0 m s–1 and his vertical speed is 2.8 m s–1.(a) Show that the total time the athlete spends in the air is about 0.6 s.Assume that his centre of gravity is at the same height at take-off and landing.(3) .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. ..................................................................................................................................................................................................................................................(b) Calculate the horizontal distance jumped by the athlete.(2) .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. ..................................................................................................................................................................................................................................................Horizontal distance = ..................................................................21*P43321A02132*Turn over(c) In reality, when the athlete lands his centre of gravity is 50 cm lower than its position at take-off. Calculate the extra horizontal distance this enables the athlete to jump.(4)....................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................Extra horizontal distance = ..................................................................(total for Question 16 = 9 marks)22*P43321A02232*17 Pile drivers have been used for centuries to push piles into the ground for use as foundations of buildings and other structures. A large mass (the driver) is raised and then dropped onto an object (the pile) which is pushed into the ground.The picture shows the pile driver that was used to build a London bridge in the 17th century.(a) (i) The driver on the pile driver above had a mass of 810 kg and could be dropped a maximum distance of 6.0 m onto the pile.Show that the energy transferred from the driver is about 50 kJ.(2)............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................ (ii) In one instance, 40% of this energy is used usefully to drive in the pile. The pile moves 0.20 m into the ground.Determine the average resistive force acting on the pile as it moves through the ground.(3)....................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................Average resistive force = .................................................................driverpile23*P43321A02332*Turn over24*P43321A02432*25*P43321A02532*Turn over *(iii) T he graph shows how the compression of the wooden cushion varies with force, as the force is applied and removed during an impact.Use the graph to explain the following: 1. the wooden cushion has to be replaced after a few hundred impacts,(2)........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................2. with each impact the temperature of the wooden cushion rises slightly.(1).................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................... (total for Question 17 = 13 marks)ForceCompressionForce appliedForce removed。
Spin Density Wave and D-Wave Superconducting Order Parameter Coexistence
a r X i v :c o n d -m a t /0312451v 1 [c o n d -m a t .s t r -e l ] 18 D e c 2003Spin Density Wave and D-Wave Superconducting Order Parameter “Coexistence”Zaira Nazario †and David I.Santiago †,⋆†Department of Physics,Stanford University,Stanford,California 94305⋆Gravity Probe B Relativity Mission,Stanford,California 94305We study the properties of a spin-density-wave antiferromagnetic mean-field ground state with d-wave superconducting (DSC)correlations.This ground state always gains energy by Cooper pairing.It would fail to superconduct at half-filling due to the antiferromagnetic gap although its particle-like excitations would be Bogolyubov-BCS quasiparticles consisting of coherent mixtures of electrons and holes.More interesting and relevant to the superconducting cuprates is the case when antiferromagnetic order is turned on weakly on top of the superconductivity.This would correspond to the onset of antiferromagnetism at a critical doping.In such a case a small gap proportional to the weak antiferromagnetic gap opens up for nodal quasiparticles,and the quasiparticle peak would be discernible.We evaluate numerically the absorption by nodal quasiparticles and the local density of states for several ground states with antiferromagnetic and d-wave superconducting correlations.PACS numbers:74.20.-z,74.20.Mn,74.72.-h,71.10.Fd,71.10.PmI.INTRODUCTIONEver since the discovery of high temperature superconductivity 1it was proposed that the supercon-ducting correlations might already exists in the antifer-romagnetic Mott insulator 2.The origin of the supercon-ducting correlations was ascribed to the large Coulombic interactions in the undoped materials.The only other large energy scale in the materials is phononic 3.While the microscopic origin of superconductivity re-mains a matter of debate 4,5,6,7,there is growing experi-mental evidence that the quasiparticles are Bogolyubov-BCS quasiparticles.Bending back of photoemis-sion bands 8fits quantitatively the BCS-Bogolyubov model 9,10.Scanning tunneling microscopy finds coher-ent quasiparticles that disperse as a coherent mixture of particles and holes 11,12.The particle and hole am-plitudes in these experiments and in inverse photoemis-sion experiments 12,13fit accurately to the theoretical Bogolyubov-BCS values calculated from the dispersion and gap measured in the normal and superconducting materials respectively.Regardless of whether the origin of superconducting correlations is exotic Coulombic physics or some more conventional mechanism,it is clear that the cuprates are BCS paired superconductors.This does not mean that the Coulomb interactions do not matter.Rather,the in-teresting and contradictory physics for underdoped ma-terials is the result of Coulomb degradation of the super-fluid density 2,4,5,6and order parameter competition be-tween superconductivity and correlated electron ground states 14,15.The degradation of the superfluid density leads to suppressed T c due to a phase instability of the superconducting order parameter 2,16,17,18,19.There are several Coulomb stabilized competing ground states such as orbital antiferromagnetism 15,stripe or charge density wave ground states 20and perhaps electronic liquid crys-tal phases 21.Regardless of which of these competing ground states are realized,there is strong experimental evidence for incommensurate electronic ordering 22,either0.5 1 1.5 2 2.5-8-6-4-2 0 2 4 6 8D e n s i t y o f S t a t e s [A r b i t r a r y U n i t s ]Energy/Hopping0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2-8-6-4-2 0 2 4 6 8D e n s i t y o f S t a t e s [A r b i t r a r y U n i t s ]Energy/HoppingFIG.1:Spectral Function for the SDW ground state without (1a)and with (1b)superconducting correlations built in.static or incipient.The evidence seems more consistent with charge-density-wave or stripe order.In the present work we will study the physics of an antiferromagnet with a strong d-wave Cooper pairing in-teraction.We do not speculate as to the origin of this superconducting interaction except to point out that inFIG.2:In the upper left side we draw two bands separatedby a gap,with the lower band partiallyfilled appropriate toa metal or superconductor.In the upper right side we drawthe situation encountered for the electronfluid under the ac-tion of an electricfield.The lower sketch illustrates the sit-uation appropriate to an insulator,where the lower band iscompletelyfilled,making conduction impossible regardless ofCooper correlations.such a model it competes with the Coulombic antiferro-magnetic physics.Both the superconductor and the anti-ferromagnet are studied in the meanfield approximation.While one can doubt the validity of such an approxima-tion at a phase transition point,it will be qualitativelycorrect within the ordered phases.Cooper pairing leading to a BCS ground state is aninstability of a Fermi liquid ground state.In this studywe apply the BCS approximation to a spin density wave(SDW)insulating ground state as it exists in the cupratesat halffilling.The resulting ground state has Cooperpairing yet it fails to superconduct due to the SDW insu-lating gap.Next we will review some well known facts inorder to understand how a state with Cooper pairs doesnot superconduct.Before doing so we emphasize thatthis only happens as a consequence of having a completelyfilled insulating band.When an electricfield is applied to a metal,it con-ducts dissipatively.The way this happens is that thecenter of mass of the Fermi sea gets displaced upwardin the unfilled metallic band23.Ohmic dissipation oc-curs because newlyfilled electronic states at the top ofthe Fermi sea get scattered into newly empty electronicstates at the bottom of the Fermi sea due to the lack ofrigidity of the Fermi liquid ground state(seefigure2).When there are Cooper correlations,the electron liquidgets displaced upward in the band too,but as long asthe displacement in energy within the band is less thanthe superconducting gap,Cooper pair correlations makethe electron liquid rigid,thus preventing scattering anddissipation.For the case of an SDW ground state at halffilling with Cooper pairing correlations there is no super-conductivity as the electronfluid cannot move upward inthe band for the band is full and there are no electronicstates to befilled unless one excites across the insulatinggap and into the conduction band(seefigure2).That the SDW insulating ground state with d-wavepairing interactions has Cooper pairing in the groundstate can be seen fromfigure1.Infigure1a we plotthe spectral function for the SDW ground state with nosuperconducting correlations.Infigure1b we plot thespectral function for the SDW ground state with super-conducting correlations.In the ground state with bothsuperconductivity and antiferromagnetism,the separa-tion between the coherence peaks is bigger as it gets con-tributions from both the SDW and superconducting gap.A prediction of this model is that the quasiparticles willbe coherent with an electron and a hole component inagreement with the BCS-Bogolyubov model.The SDW ground state with d-wave Cooper pairing(SDW-DSC)will become superconducting when doped.At the mean-field level,without worrying about self con-sistency,the chemical potential will jump to the ap-propriate band and there will be a low superfluid den-sity superconductor.Whether this physics is correctfor the cuprates is controversial.There is experimen-tal evidence for the chemical potential staying pinned atmidgap due to spectral redistribution of states towardmidgap states24.There is also experimental evidence forchemical potential shifts in the cuprates,in the sameway as in regular semiconductor materials25.Indepen-dently of whether the SDW-DSC ground state has chem-ical potential shifts or not,the physics of an insulatorwith Cooper pairing correlations is interesting.For ourstudy we have the cuprates in mind.For these materials,some phenomenology of this form seems to apply2,butit would be interesting if this physics were to be realizedin nature irrespective of the cuprate problem.In the present work we willflip the problem around.We will start with a d-wave superconductor(DSC)andbegin turning on SDW antiferromagnetic order on top ofthe superconductivity.In this limit,the complicationsmentioned in the previous paragraph are nonexistent.Aslow turning on of SDW order on top of the supercon-ductivity will show up as a shift of the antinodal gap anda gapping of the nodal quasiparticles.The latter shouldbe a signal much easier to pick out than the gap shift.The gapping of the nodal quasiparticles is not a uniqueprediction of antiferromagnetic ordering on top of the su-perconductivity,as such a gapping can be produced bydisorder.On the other hand,the coherence of the gapped“nodal”quasiparticles would be nonexistent for a disor-dered gap and is thus a unique signature of antiferromag-netic ordering developing on top of the superconductivity.Therefore,if a quasiparticle peak is discernible,and thebroadening is less than the disorder-induced broadening(>∼ 2/2m∆x2≃350meV for∆x∼1nm,appropriateto the cuprates),then the gap is a long range orderedgap and not a disordered gap.Another unique signatureof an SDW gap is that the gap will open exactly at the10 20 30 40 50 60-6-4-2 0 2 4 6[A r b i t r a r y U n i t s ]5 10 15 20 25 30-6-4-2 0 2 4 65 10 15 20 25 30 35-6-4-2 0 2 4 6S t r e n g t h0.2 SDW gap5 10 15 20 25 30 35-6-4-2 0 2 4 60.3 SDW gap0 5 10 15 20 25 30 35-6-4-20 24 6A b s o r p t i o nEnergy/Hopping0.6 SDW gap1020 30 40 50 60 70-6-4-20 24 6Energy/Hopping0.0 SDW gap 0.1 SDW gap 0.2 SDW gap 0.3 SDW gap 0.6 SDW gapFIG.3:Gapping of the nodal quasiparticles pole as the SDW order develops.doping where the antiferromagnetism starts.There are experimental suggestions of antiferromag-netism competing with superconductivity in the deep un-derdoped regime in the cuprates.For example,measure-ments show the nodal quasiparticle peaks surviving right up to the doping where antiferromagnetism starts.The spectral weight of such peaks diminishes with decreas-ing doping,consistent with spectral weight being robbed from the superconducting long range order by a compet-ing long range order such as antiferromagnetism 26.If one looks in the antiferromagnetically ordered dopings,there are experimental suggestions of a competing order pa-rameter that conducts efficiently.Most strikingly,there5 10 15 20 25 30-6-4-2 0 2 4 6[A r b i t r a r y U n i t s ]5 10 15 20 25 30-6-4-2 0 2 4 60 5 10 15 20 25 30 35-6-4-20 24 6A b s o r p t i o n S t r e n g t hEnergy/Hopping0.6 SDW gap510 15 20 25 30 35-6-4-20 24 6Energy/Hopping0.0 SDW gap 0.3 SDW gap 0.6 SDW gapFIG.4:Shift of the antinodal gap as the SDW order develops.are measurements of metallic conduction even below the Neel ordering temperature 27.The gapping of the nodal quasiparticles pole as the SDW order develops on top of the superconductivity is shown in figure 3for different values of the SDW gap.The reason we only have a quasiparticle sharp pole is that we have not modeled the realistic electronic self energies relevant to the cuprates as they are irrelevant to the pointof principle we are making.Their only effect will be to broaden the quasiparticle peaks and add an incoherent background with the phenomenological features.In fig-ure 4we plot the shift of the antinodal gap as the SDW gap turns on.In figure 5we plot the spectral density of states in a d-wave superconductor as the SDW gap is turned on.The superconductor with no SDW gap does not have a true gap because of its d-wave symmetry.This is seen in the familiar V-shaped collapse at zero energy.As the SDW gap is turned on,we see the V-shape flatten and expand as a signature of the opening of the antifer-romagnetic gap.II.HUBBARD MODEL WITH D-W A VE ATTRACTIVE INTERACTIONSFor the cuprate problem,the two large effects are the antiferromagnetic,or Coulombic,physics and the strong superconductivity.Hence we will start from a phe-nomenological Hamiltonian which is a Hubbard model with a d-wave electronic interaction.This interaction will give rise to d-wave superconductivity when we make the mean-field BCS approximation.The Hamiltonian isH =k,σ(ǫ k −µ)c †k,σck,σ+U0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6-8-6-4-22 4 6 8[A r b i t r a r y U n i t s ]0.0 SDW gap0.20.4 0.6 0.8 1 1.2 1.4 1.6-8-6-4-2 0 2 4 6 80.1 SDW gap0 0.2 0.4 0.6 0.8 11.2 1.4 1.6-8-6-4-22 4 6 8S t a t e s0.2 SDW gap0.20.4 0.6 0.8 1 1.2 1.4 1.6 1.8-8-6-4-2 0 2 4 6 80.3 SDW gap0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2-8-6-4-2 0 2 4 6 8D e n s i t y o fEnergy/Hopping0.6 SDW gap0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2-8-6-4-2 0 2 4 6 8Energy/Hopping0.0 SDW gap 0.1 SDW gap 0.2 SDW gap 0.3 SDW gap 0.6 SDW gapFIG.5:Spectral density of states for a d-wave superconductor as the SDW gap increases.where c †k,σ,ck,σare the electronic creation and destruc-tion operators with momentum k and spin σ,ǫ k is the kinetic energy,µthe chemical potential,and U is the Hubbard repulsion.We are working in a spatial lattice with N sites.The last term is an electronic interaction chosen in the reduced BCS form 9,which will be used to stabilize superconductivity.In order to have d-wavesuperconductivity we choose V ( k 1, k 2)=V 0(cosk 1x −cosk 1y )(cosk 2x −cosk 2y ).This phenomenological Hamil-tonian can have a mean-field SDW ground state and a mean-field DSC ground state.It can be used to study the turning on of DSC correlations on top of an SDW ground state,or the turning on of SDW order on top of the superconductivity.We will analyze this Hamiltonian by imposing an SDW meanfield condition,which is stabilized by the Hubbard term.This will be followed by a DSC mean-field con-dition,which is stabilized by the reduced BCS d-wave interaction.While the use of two mean-field conditions is not common,it has important precedents.It was used by P.W.Anderson28in his study of the role of plasmons in restoring gauge invariance to the BCS ground state.In this work he invented the Anderson-Higgs mechanism29. He solved for the properties of the electron system im-posing a mean-field condition on the electron density,as in the study of electron correlations by Sawada,et al30 and a BCS electron pairing mean-field condition9.The Hubbard interaction stabilizes the mean-field or-derσSN≡ k c† k+ Q,σc k,σ (2)where Q=(π,π)is the commensurate ordering wave vector and S is the average magnetic moment per site. Other ordering wave vectors are possible for spin and/or charge,i.e.stripe,order parameters but we do not con-sider them in our study.When we impose this conditionon the Hamiltonian and neglectfluctuation terms,the Hamiltonian becomesH= k,σ(ǫ k−µ)c† k,σc k,σ+UNS2−US k,σσc† k+ Q,σc k,σ+ k1, k2V( k1, k2)c† k1,↑c†− k1,↓c− k2,↓c k2,↑(3)We see that by ordering antiferromagnetically we gain variational energy−UNS2if self-consistency can be achieved.We next impose the mean-field d-wave Cooper pairing∆k2≡(cosk2x−cosk2y)V0 k1(cosk1x−cosk1y) c† k1,↑c†− k1,↓ ≡∆0(cosk2x−cosk2y)(4) Then the Hamiltonian becomesH= k,σ(ǫ k−µ)c† k,σc k,σ+UNS2−US k,σσc† k+ Q,σc k,σ−∆20V0+ k′∆ k c† k,↑c†− k,↓+c− k,↓c k,↑−c† k+ Q,↑c†− k− Q,↓−c− k− Q,↓c k+ Q,↑ (6)where the prime on the summation sign means that the sum is restricted to the wave vectors in the magneticzone.ǫ+k≡(ǫ k+ǫ k+ Q)/2andǫ− k≡(ǫ k−ǫ k+ Q)/2.The last term in the superconducting interaction is negative because∆k+ Q=−∆k.In order to diagonalize the mag-netic part we define the Bogolyubov operatorsbk,σ=αkck,σ−σβ k c k+ Q,σ(7)bk+ Q,σ=αkck+ Q,σ+σβkck,σ(8) If we chooseα2k=1Ek β2 k=1Ek (9)E2k=(ǫ−k)2+U2S2(10) the Hamiltonian becomesH= k,σ′ (ǫ+ k−µ)(b† k,σb k,σ+b† k+ Q,σb k+ Q,σ)+Ek(b†k,σbk,σ−b† k+ Q,σb k+ Q,σ) +UNS2−∆207Bk+ Q,σ=u−kbk+ Q,σ−σv− k b† k+ Q,¯σ(13)If we choose(u±k )2=1E±k (14)(v±k )2=1E±k (15)(E±k )2=(ǫ+k−µ±E k)2+∆2 k(16)the Hamiltonian then becomesH= k,σ′ E+ k B† k,σB k,σ+E− k B† k+ Q,σB k+ Q,σ+UNS2−∆20U= k ǫ+ k−µ+E k E− k E k (18)from the antiferromagnetic self-consistency condition(2) and−2E+k +12πi ∞−∞dω√πN k(u+ k)2E−E−k+iη−(v+k)2E+E−k−iη(23)The local spectral density function follows from31A( x,E)=−igap to be0.3.The antiferromagnetic gap is chosen any-where between0and0.6,usually with jumps of0.1.We have nearest neighbor hopping only.These values need not be realistic;they are just chosen to illustrate the ef-fect.Similarly,if we Fourier transform the Green’s function (20)in both time and space,we obtain the retarded prop-agator in the wavevector energy representation.G( k,E)=1E−E+k+iη+(u−k)2E+E+k−iη−(v−k)2πIm G( k,E)(26)vs.energy.Energy units,values and uncertainties are chosen as described for the local density of states.V.CONCLUSIONSWe studied a meanfield Hamiltonian with two mean field order parameters.The Hamiltonian contains a spin-density-wave antiferromagnetic meanfield stabilized by a Hubbard interaction and a d-wave Cooper pairing mean field stabilized by a phenomenological d-wave interac-tion.The two order parameters can coexist and the SDW ground state always gains energy by Cooper pairing when the d-wave interaction is attractive and nonzero.The SDW ground state with Cooper pairing fails to super-conduct at half-filling due to the antiferromagnetic gap. Its particle-like excitations are Bogolyubov-BCS quasi-particles consisting of coherent mixtures of electrons and holes.Of greater interest and relevance to the superconduct-ing cuprates is the case when antiferromagnetic order is turned on weakly on top of the superconductivity.This would correspond to the onset of antiferromagnetism at a critical doping.In such a case a small gap proportional to the weak antiferromagnetic gap opens up for nodal quasiparticles,and the quasiparticle peak would be dis-cernible.While the gapping of the nodal quasiparticle could be caused by a large enough disorder,such a dis-order would broaden the quasiparticle peak so much as to make it invisible.A unique signature of antiferromag-netic gapping of the nodal quasiparticles is that it will turn on always at the doping when antiferromagnetism starts while disorder gapping will turn on at different sample dependent dopings.We wrote down the exact expressions for the Green’s function for the system with coexisting SDW and DSC order parameters.These are evaluated numerically in a 1000×1000momentum lattice with.01energy resolu-tion in units of the lattice hopping.From the imaginary parts of the Green’s functions we obtained the absorption by nodal quasiparticles and the local density of states. In our work we did not worry about having self-consistency.This neglect does not affect our results when the two order parameters are nonzero,but it will affect whether the order parameters are nonzero or not,and what the gap values are.Self-consistency will be im-portant in studying how the two order parameters com-pete and if and how they steal spectral weight from each other.Self-consistency might also affect how the SDW-DSC ground state behaves when doped from half-filling. Intuitively one expects chemical potential shifts,but it is not certain that this would be the case.All these is-sues should be studied carefully and we postpone them for future work.Acknowledgments Zaira Nazario is a Ford Founda-tion predoctoral fellow.She was supported by the Ford Foundation and by the School of Humanities and Science at Stanford University.David I.Santiago was supported by NASA Grant NAS8-39225to Gravity Probe B.1G.J.Bednorz and K.A.Muller,Z.Phys.B64,189(1986); M.K.Wu et.al.,Phys.Rev.Lett.,58,908(1987);H. 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A.Bernevig,et.al.e-print arXiv:cond-mat/0304419 (2003).20S.A.Kivelson and V.J.Emery,Synthetic Metals80,151 (1996).21S.A.Kivelson,et.al.,Nature393,550(1998).22J.M.Tranquada,et.al.,Phys.Rev.B.54,7489(1996). 23N.F.Mott and H.Jones,The Theory of the Properties of Metals and Alloys,Dover Pubns(June1958).24S.Uchida,et.al.,Phys.Rev.B.43,7942(1991).25M.A.Kastner,et.al.,Rev.Mod.Phys.70,897(1998). 26T.Yoshida,et.al.,Phys.Rev.Lett.91,027001(2003). 27Y.Ando,et.al.,J.Low.Temp.Phys.131,793(2003);Y.Ando,ICTP Workshop on Intrinsic Multiscale Structure and Dynamics in Complex Electronic Oxides,Trieste,July 2002.(To be published in the Proceedings of the ICTP Workshop as a World Scientific book.);S.Komiya,et.al., Phys.Rev.B65,214535(2002).28P.W.Anderson,Phys.Rev.110,827(1958);P.W.An-derson,Phys.Rev.112,1900(1958).29P.W.Higgs,Phys.Rev.Lett.13,508(1964);G.S.Gu-ralnik,et.al.,Phys.Rev.Lett.13,585(1964).30K.Sawada,et.al.,Phys.Rev.108,507(1957).31A.L.Fetter and J.D.Walecka,Quantum Theory of Many-Particle Systems,Dover Pubns(June2003).。
a level 高中物理 知识点 英文
a level 高中物理知识点英文Physics is a fundamental science that underpins our understanding of the natural world around us. At the high school level, the study of physics lays the groundwork for more advanced studies in science and technology. The A Level physics curriculum in particular covers a wide range of topics that provide students with a comprehensive understanding of the principles governing the physical universe.One of the key knowledge points in A Level physics is mechanics, which deals with the motion of objects and the forces that act upon them. This includes the study of kinematics, which describes the motion of objects in terms of position, velocity, acceleration, and time. Students learn to apply the equations of motion to analyze the behavior of objects under the influence of forces such as gravity, friction, and tension. They also explore the concepts of momentum, impulse, and conservation of momentum, which are crucial in understanding collisions and other dynamic phenomena.Another important area in A Level physics is waves and optics. This covers the properties and behavior of different types of waves,including transverse waves like light and longitudinal waves like sound. Students learn about the principles of wave interference, diffraction, and refraction, and how these phenomena can be applied in technologies like fiber optic communication and medical imaging. The study of optics also includes the behavior of light, including the laws of reflection and refraction, and the operation of optical devices such as mirrors and lenses.Electricity and magnetism are also core topics in the A Level physics curriculum. Students delve into the fundamental concepts of electric charge, electric fields, and electric potential, as well as the principles of electric circuits and the flow of electric current. They also explore the relationship between electricity and magnetism, including the generation of electromagnetic induction and the workings of electric motors and generators.Another key knowledge point in A Level physics is thermal physics, which covers the behavior of heat and temperature, as well as the concepts of thermal energy, thermal expansion, and the laws of thermodynamics. Students learn to apply these principles to understand phenomena like the operation of heat engines, the transfer of heat, and the behavior of gases.The A Level physics curriculum also includes the study of modern physics, which encompasses the groundbreaking developments inthe field during the 20th century. This includes the theory of special relativity, which describes the relationship between space, time, and the speed of light, as well as the principles of quantum mechanics, which govern the behavior of matter and energy at the atomic and subatomic scales.In addition to these core knowledge points, the A Level physics curriculum also covers a range of other topics, such as astrophysics, nuclear physics, and particle physics. These areas delve into the structure and behavior of the universe, from the smallest subatomic particles to the largest celestial bodies.Throughout the A Level physics curriculum, students are not only expected to understand the theoretical concepts but also to apply them in practical, real-world situations. This involves the development of skills in experimental design, data analysis, and problem-solving. Students learn to design and conduct experiments, collect and interpret data, and use their knowledge of physics principles to explain and predict physical phenomena.The study of A Level physics also fosters the development of critical thinking and analytical skills, as students are required to engage in complex problem-solving and decision-making processes. They learn to break down problems, identify the relevant physical principles, and apply them to arrive at solutions. These skills are highly valued ina wide range of fields, from engineering and technology to finance and business.Overall, the A Level physics curriculum provides students with a comprehensive and rigorous understanding of the physical world. By mastering the key knowledge points and developing essential skills, students are well-equipped to pursue further studies in science, technology, engineering, and mathematics (STEM) fields, or to apply their knowledge in a variety of professional contexts. The study of A Level physics not only enhances students' scientific understanding but also prepares them for the challenges and opportunities of the modern world.。
2025届高考英语一轮总复习选择性必修第四册Unit1ScienceFiction教师用书
UNIT 1 SCIENCE FICTION一、阅读词汇——在词块中明义1．science fiction科幻小说2．annual bonus年终红利3．a ridiculous rumour 荒谬的谣言4．a man of integrity一个诚恳正直的人5．with grace and dignity文静而庄重6．an absurd idea 一个荒唐的想法7．bus fares公交车车费8．excuse for inaction不实行措施的理由9．alien forces in the region 该地区的外国军队10．grip the rope 抓紧绳子11．be filled with hazy frost 充溢着朦胧的雾霭12．the maximum height 最高高度13．pay a huge salary付一大笔薪水14．fall backwards仰面摔倒15．fetch some books 拿来一些书二、表达词汇——在语境中活用(一)在括号内写出蓝体词汇在语境中的汉语意思1．Some of the studies show positive results, whereas others do not.(conj.然而)2．We go and do the weekly shopping every Thursday.(adj.每周的)3．The company wants to keep down labour costs.(n.劳动)4．Many people were not satisfied with the pace of change.(n.速度)(二)写出蓝体词汇的语境之义及拓展形式1．She made an appointment for her son to see the doctor.(n.预约)拓展：appoint v．任命；委任；支配→appointed adj.指定的；约定的2．His guilty expression confirmed my suspicions.(adj.内疚的)拓展：guilt n．内疚；懊悔；犯罪3．The population explodes to 40,000 during the tourist season.(vi.激增) 拓展：explosion n．爆炸；爆发；激增4．I dismissed the problem from my mind.(vt.消退)拓展：dismissal n．解雇；撤职5．He declared he would not run for a second term as president.(vt.宣称) 拓展：declaration n．申报(单)；宣布；公告6．From this you can calculate the total mass in the Galaxy.(vt.计算)拓展：calculation n．计算→calculator n．计算器7．We have a relationship infinitely superior to those of many of our friends.(adj.更好的)拓展：superiority n．优越感；优势；优越(性)8．I taught my daughter how to do division at the age of six.(n.除法)拓展：divide v．(使)分开9．They urged Congress to approve plans for their reform programme.(vt.力劝) 拓展：urgency n．紧迫；急事→urgent adj.紧急的；迫切的→urgently adv.迫切地；紧急地10．The survey used a random sample of two thousand people across the Midwest.(adj.随机的)拓展：randomly adv.随机；随意；未加支配地三、词块短语——在语境中辨义活用写出或选出加蓝部分在语境中的汉语意思1．The new product had been tested out before it was put on the market.检验2．The organization encourages members to meet on a regular basis as well as provides them with financial support.定期3．Although she is my teacher, Ms Wang and I are more like friends. 更像是4．Do you know what this product is? Or rather，what it does？更准确地说5．After his defeat, many of his supporters fell away.消逝6．Their opinion on the accident conflicted with ours.与……冲突或抵触7．This model of 5G mobile phone is far superior to any others.比……更好8．We have an urge to give advice immediately to make the person feel better and try to fix the problem.有剧烈的欲望9．Miss Smith is leaving to get married and Miss Jones will take over the class.A A．接手B．汲取C．呈现D．占据10．You can't expect everything to turn out as you wish.DA．关掉B．熄灭 C．在场D．结果是四、经典句式——在佳句背诵中品悟规则用法2.3.4.教材原句Night came as if a lamp was being turned out, and in another moment came the day.(as if引导方式状语从句)夜幕驾临了，仿佛一盏灯正在熄灭，转瞬间，白昼就来临了。
第四届冷原子会议会议安排July 5
[P16]
Jing Qian（钱静）
Efficient production of polar molecular Bose–Einstein condensates via an all-optical R-type atom–molecule adiabatic passage
41
[P17]
31
[P07]
Haichao Zhang（张海潮）
Demonstration of Neutral Atom Guiding via Radio-Frequency Field
32
[P08]
Shuyu Zhou（周蜀渝）
Double-well Array Trapping Atoms Based on Binary Optics ethod
会议安排July 5, Monday
Opening Ceremony
Presider
Liang Liu（刘亮）
8:30-9:00
Yuzhu Wang（王育竹）and Chaohui Ye（叶朝辉）
Opening Remarks
Sec. A
Presider
Li You（尤力）
9:00-9:30
Jun Ye（叶军）
Xing-Dong Zhao（赵兴东）
A magical polarization orientation for canceling the dipole-dipole
interaction in ultracold Bosonic dipolar gases
42
[P18]
Cheng-ling Bian（边成玲）
46
[P22]
K. Zhang（张可烨）
量子力学索引英汉对照
21-centimeter line, 21厘米线AAbsorption, 吸收Addition of angular momenta, 角动量叠加Adiabatic approximation, 绝热近似Adiabatic process, 绝热过程Adjoint, 自伴的Agnostic position, 不可知论立场Aharonov-Bohm effect, 阿哈罗诺夫—玻姆效应Airy equation, 艾里方程；Airy function, 艾里函数Allowed energy, 允许能量Allowed transition, 允许跃迁Alpha decay, α衰变；Alpha particle, α粒子Angular equation, 角向方程Angular momentum, 角动量Anomalous magnetic moment, 反常磁矩Antibonding, 反键Anti-hermitian operator, 反厄米算符Associated Laguerre polynomial, 连带拉盖尔多项式Associated Legendre function, 连带勒让德多项式Atoms, 原子Average value, 平均值Azimuthal angle, 方位角Azimuthal quantum number, 角量子数BBalmer series, 巴尔末线系Band structure, 能带结构Baryon, 重子Berry's phase, 贝利相位Bessel functions, 贝塞尔函数Binding energy, 束缚能Binomial coefficient, 二项式系数Biot-Savart law, 毕奥—沙法尔定律Blackbody spectrum, 黑体谱Bloch's theorem, 布洛赫定理Bohr energies, 玻尔能量；Bohr magneton, 玻尔磁子；Bohr radius, 玻尔半径Boltzmann constant, 玻尔兹曼常数Bond, 化学键Born approximation, 玻恩近似Born's statistical interpretation, 玻恩统计诠释Bose condensation, 玻色凝聚Bose-Einstein distribution, 玻色—爱因斯坦分布Boson, 玻色子Bound state, 束缚态Boundary conditions, 边界条件Bra, 左矢Bulk modulus, 体积模量CCanonical commutation relations, 正则对易关系Canonical momentum, 正则动量Cauchy's integral formula, 柯西积分公式Centrifugal term, 离心项Chandrasekhar limit, 钱德拉赛卡极限Chemical potential, 化学势Classical electron radius, 经典电子半径Clebsch-Gordan coefficients, 克—高系数Coherent States, 相干态Collapse of wave function, 波函数塌缩Commutator, 对易子Compatible observables, 对易的可观测量Complete inner product space, 完备内积空间Completeness, 完备性Conductor, 导体Configuration, 位形Connection formulas, 连接公式Conservation, 守恒Conservative systems, 保守系Continuity equation, 连续性方程Continuous spectrum, 连续谱Continuous variables, 连续变量Contour integral, 围道积分Copenhagen interpretation, 哥本哈根诠释Coulomb barrier, 库仑势垒Coulomb potential, 库仑势Covalent bond, 共价键Critical temperature, 临界温度Cross-section, 截面Crystal, 晶体Cubic symmetry, 立方对称性Cyclotron motion, 螺旋运动DDarwin term, 达尔文项de Broglie formula, 德布罗意公式de Broglie wavelength, 德布罗意波长Decay mode, 衰变模式Degeneracy, 简并度Degeneracy pressure, 简并压Degenerate perturbation theory, 简并微扰论Degenerate states, 简并态Degrees of freedom, 自由度Delta-function barrier, δ势垒Delta-function well, δ势阱Derivative operator, 求导算符Determinant, 行列式Determinate state, 确定的态Deuterium, 氘Deuteron, 氘核Diagonal matrix, 对角矩阵Diagonalizable matrix, 对角化Differential cross-section, 微分截面Dipole moment, 偶极矩Dirac delta function, 狄拉克δ函数Dirac equation, 狄拉克方程Dirac notation, 狄拉克记号Dirac orthonormality, 狄拉克正交归一性Direct integral, 直接积分Discrete spectrum, 分立谱Discrete variable, 离散变量Dispersion relation, 色散关系Displacement operator, 位移算符Distinguishable particles, 可分辨粒子Distribution, 分布Doping, 掺杂Double well, 双势阱Dual space, 对偶空间Dynamic phase, 动力学相位EEffective nuclear charge, 有效核电荷Effective potential, 有效势Ehrenfest's theorem, 厄伦费斯特定理Eigenfunction, 本征函数Eigenvalue, 本征值Eigenvector, 本征矢Einstein's A and B coefficients, 爱因斯坦A,B系数；Einstein's mass-energy formula, 爱因斯坦质能公式Electric dipole, 电偶极Electric dipole moment, 电偶极矩Electric dipole radiation, 电偶极辐射Electric dipole transition, 电偶极跃迁Electric quadrupole transition, 电四极跃迁Electric field, 电场Electromagnetic wave, 电磁波Electron, 电子Emission, 发射Energy, 能量Energy-time uncertainty principle, 能量—时间不确定性关系Ensemble, 系综Equilibrium, 平衡Equipartition theorem, 配分函数Euler's formula, 欧拉公式Even function, 偶函数Exchange force, 交换力Exchange integral, 交换积分Exchange operator, 交换算符Excited state, 激发态Exclusion principle, 不相容原理Expectation value, 期待值FFermi-Dirac distribution, 费米—狄拉克分布Fermi energy, 费米能Fermi surface, 费米面Fermi temperature, 费米温度Fermi's golden rule, 费米黄金规则Fermion, 费米子Feynman diagram, 费曼图Feynman-Hellman theorem, 费曼—海尔曼定理Fine structure, 精细结构Fine structure constant, 精细结构常数Finite square well, 有限深方势阱First-order correction, 一级修正Flux quantization, 磁通量子化Forbidden transition, 禁戒跃迁Foucault pendulum, 傅科摆Fourier series, 傅里叶级数Fourier transform, 傅里叶变换Free electron, 自由电子Free electron density, 自由电子密度Free electron gas, 自由电子气Free particle, 自由粒子Function space, 函数空间Fusion, 聚变Gg-factor, g—因子Gamma function, Γ函数Gap, 能隙Gauge invariance, 规范不变性Gauge transformation, 规范变换Gaussian wave packet, 高斯波包Generalized function, 广义函数Generating function, 生成函数Generator, 生成元Geometric phase, 几何相位Geometric series, 几何级数Golden rule, 黄金规则"Good" quantum number, “好”量子数"Good" states, “好”的态Gradient, 梯度Gram-Schmidt orthogonalization, 格莱姆—施密特正交化法Graphical solution, 图解法Green's function, 格林函数Ground state, 基态Group theory, 群论Group velocity, 群速Gyromagnetic railo, 回转磁比值HHalf-integer angular momentum, 半整数角动量Half-life, 半衰期Hamiltonian, 哈密顿量Hankel functions, 汉克尔函数Hannay's angle, 哈内角Hard-sphere scattering, 硬球散射Harmonic oscillator, 谐振子Heisenberg picture, 海森堡绘景Heisenberg uncertainty principle, 海森堡不确定性关系Helium, 氦Helmholtz equation, 亥姆霍兹方程Hermite polynomials, 厄米多项式Hermitian conjugate, 厄米共轭Hermitian matrix, 厄米矩阵Hidden variables, 隐变量Hilbert space, 希尔伯特空间Hole, 空穴Hooke's law, 胡克定律Hund's rules, 洪特规则Hydrogen atom, 氢原子Hydrogen ion, 氢离子Hydrogen molecule, 氢分子Hydrogen molecule ion, 氢分子离子Hydrogenic atom, 类氢原子Hyperfine splitting, 超精细分裂IIdea gas, 理想气体Idempotent operaror, 幂等算符Identical particles, 全同粒子Identity operator, 恒等算符Impact parameter, 碰撞参数Impulse approximation, 脉冲近似Incident wave, 入射波Incoherent perturbation, 非相干微扰Incompatible observables, 不对易的可观测量Incompleteness, 不完备性Indeterminacy, 非确定性Indistinguishable particles, 不可分辨粒子Infinite spherical well, 无限深球势阱Infinite square well, 无限深方势阱Inner product, 内积Insulator, 绝缘体Integration by parts, 分部积分Intrinsic angular momentum, 内禀角动量Inverse beta decay, 逆β衰变Inverse Fourier transform, 傅里叶逆变换KKet, 右矢Kinetic energy, 动能Kramers' relation, 克莱默斯关系Kronecker delta, 克劳尼克δLLCAO technique, 原子轨道线性组合法Ladder operators, 阶梯算符Lagrange multiplier, 拉格朗日乘子Laguerre polynomial, 拉盖尔多项式Lamb shift, 兰姆移动Lande g-factor, 朗德g—因子Laplacian, 拉普拉斯的Larmor formula, 拉摩公式Larmor frequency, 拉摩频率Larmor precession, 拉摩进动Laser, 激光Legendre polynomial, 勒让德多项式Levi-Civita symbol, 列维—西维塔符号Lifetime, 寿命Linear algebra, 线性代数Linear combination, 线性组合Linear combination of atomic orbitals, 原子轨道的线性组合Linear operator, 线性算符Linear transformation, 线性变换Lorentz force law, 洛伦兹力定律Lowering operator, 下降算符Luminoscity, 照度Lyman series, 赖曼线系MMagnetic dipole, 磁偶极Magnetic dipole moment, 磁偶极矩Magnetic dipole transition, 磁偶极跃迁Magnetic field, 磁场Magnetic flux, 磁通量Magnetic quantum number, 磁量子数Magnetic resonance, 磁共振Many worlds interpretation, 多世界诠释Matrix, 矩阵；Matrix element, 矩阵元Maxwell-Boltzmann distribution, 麦克斯韦—玻尔兹曼分布Maxwell’s equations, 麦克斯韦方程Mean value, 平均值Measurement, 测量Median value, 中位值Meson, 介子Metastable state, 亚稳态Minimum-uncertainty wave packet, 最小不确定度波包Molecule, 分子Momentum, 动量Momentum operator, 动量算符Momentum space wave function, 动量空间波函数Momentum transfer, 动量转移Most probable value, 最可几值Muon, μ子Muon-catalysed fusion, μ子催化的聚变Muonic hydrogen, μ原子Muonium, μ子素NNeumann function, 纽曼函数Neutrino oscillations, 中微子振荡Neutron star, 中子星Node, 节点Nomenclature, 术语Nondegenerate perturbationtheory, 非简并微扰论Non-normalizable function, 不可归一化的函数Normalization, 归一化Nuclear lifetime, 核寿命Nuclear magnetic resonance, 核磁共振Null vector, 零矢量OObservable, 可观测量Observer, 观测者Occupation number, 占有数Odd function, 奇函数Operator, 算符Optical theorem, 光学定理Orbital, 轨道的Orbital angular momentum, 轨道角动量Orthodox position, 正统立场Orthogonality, 正交性Orthogonalization, 正交化Orthohelium, 正氦Orthonormality, 正交归一性Orthorhombic symmetry, 斜方对称Overlap integral, 交叠积分PParahelium, 仲氦Partial wave amplitude, 分波幅Partial wave analysis, 分波法Paschen series, 帕邢线系Pauli exclusion principle, 泡利不相容原理Pauli spin matrices, 泡利自旋矩阵Periodic table, 周期表Perturbation theory, 微扰论Phase, 相位Phase shift, 相移Phase velocity, 相速Photon, 光子Planck's blackbody formula, 普朗克黑体辐射公式Planck's constant, 普朗克常数Polar angle, 极角Polarization, 极化Population inversion, 粒子数反转Position, 位置；Position operator, 位置算符Position-momentum uncertainty principles, 位置—动量不确定性关系Position space wave function, 坐标空间波函数Positronium, 电子偶素Potential energy, 势能Potential well, 势阱Power law potential, 幂律势Power series expansion, 幂级数展开Principal quantum number, 主量子数Probability, 几率Probability current, 几率流Probability density, 几率密度Projection operator, 投影算符Propagator, 传播子Proton, 质子QQuantum dynamics, 量子动力学Quantum electrodynamics, 量子电动力学Quantum number, 量子数Quantum statics, 量子统计Quantum statistical mechanics, 量子统计力学Quark, 夸克RRabi flopping frequency, 拉比翻转频率Radial equation, 径向方程Radial wave function, 径向波函数Radiation, 辐射Radius, 半径Raising operator, 上升算符Rayleigh's formula, 瑞利公式Realist position, 实在论立场Recursion formula, 递推公式Reduced mass, 约化质量Reflected wave, 反射波Reflection coefficient, 反射系数Relativistic correction, 相对论修正Rigid rotor, 刚性转子Rodrigues formula, 罗德里格斯公式Rotating wave approximation, 旋转波近似Rutherford scattering, 卢瑟福散射Rydberg constant, 里德堡常数Rydberg formula, 里德堡公式SScalar potential, 标势Scattering, 散射Scattering amplitude, 散射幅Scattering angle, 散射角Scattering matrix, 散射矩阵Scattering state, 散射态Schrodinger equation, 薛定谔方程Schrodinger picture, 薛定谔绘景Schwarz inequality, 施瓦兹不等式Screening, 屏蔽Second-order correction, 二级修正Selection rules, 选择定则Semiconductor, 半导体Separable solutions, 分离变量解Separation of variables, 变量分离Shell, 壳Simple harmonic oscillator, 简谐振子Simultaneous diagonalization, 同时对角化Singlet state, 单态Slater determinant, 斯拉特行列式Soft-sphere scattering, 软球散射Solenoid, 螺线管Solids, 固体Spectral decomposition, 谱分解Spectrum, 谱Spherical Bessel functions, 球贝塞尔函数Spherical coordinates, 球坐标Spherical Hankel functions, 球汉克尔函数Spherical harmonics, 球谐函数Spherical Neumann functions, 球纽曼函数Spin, 自旋Spin matrices, 自旋矩阵Spin-orbit coupling, 自旋—轨道耦合Spin-orbit interaction, 自旋—轨道相互作用Spinor, 旋量Spin-spin coupling, 自旋—自旋耦合Spontaneous emission, 自发辐射Square-integrable function, 平方可积函数Square well, 方势阱Standard deviation, 标准偏差Stark effect, 斯塔克效应Stationary state, 定态Statistical interpretation, 统计诠释Statistical mechanics, 统计力学Stefan-Boltzmann law, 斯特番—玻尔兹曼定律Step function, 阶跃函数Stem-Gerlach experiment, 斯特恩—盖拉赫实验Stimulated emission, 受激辐射Stirling's approximation, 斯特林近似Superconductor, 超导体Symmetrization, 对称化Symmetry, 对称TTaylor series, 泰勒级数Temperature, 温度Tetragonal symmetry, 正方对称Thermal equilibrium, 热平衡Thomas precession, 托马斯进动Time-dependent perturbation theory, 含时微扰论Time-dependent Schrodinger equation, 含时薛定谔方程Time-independent perturbation theory, 定态微扰论Time-independent Schrodinger equation, 定态薛定谔方程Total cross-section, 总截面Transfer matrix, 转移矩阵Transformation, 变换Transition, 跃迁；Transition probability, 跃迁几率Transition rate, 跃迁速率Translation,平移Transmission coefficient, 透射系数Transmitted wave, 透射波Trial wave function, 试探波函数Triplet state, 三重态Tunneling, 隧穿Turning points, 回转点Two-fold degeneracy , 二重简并Two-level systems, 二能级体系UUncertainty principle, 不确定性关系Unstable particles, 不稳定粒子VValence electron, 价电子Van der Waals interaction, 范德瓦尔斯相互作用Variables, 变量Variance, 方差Variational principle, 变分原理Vector, 矢量Vector potential, 矢势Velocity, 速度Vertex factor, 顶角因子Virial theorem, 维里定理WWave function, 波函数Wavelength, 波长Wave number, 波数Wave packet, 波包Wave vector, 波矢White dwarf, 白矮星Wien's displacement law, 维恩位移定律YYukawa potential, 汤川势ZZeeman effect, 塞曼效应。
Pentaquarks五夸克态.ppt
Bo-Qiang Ma (马伯强)
PKU (北京大学物理学院)
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August 14, 2004 talk at CCAST Wokshop on QCD and RHIC Physics
In Collaboration with B. Wu
Hep-ph/0312041, PRD69(2004)077501 Hep-ph/0312326, PLB586（2004）62 Hep-ph/0311331, Hep-ph/0402244 Hep-ph/0408121 all to appear in PRD
n K- (K+n)
an additional K+ is detected to reduce background for the missing mass spectrum and real photon is used instead of virtual photon.
12
What is a Pentaquark
• The corrections to the Gell-Mann-Okubo relations of baryons masses in SU(3) Skyrmen model are considered.
• The results could be regarded as a signal for the existence of the SU(3) rotation excitation states of baryons: 27-plet, 10*-let, and 35-let.
– MIT bag model predictions: MZ 1.7 GeV
• L(1405): molecular meson-baryon state uudsu? – interpretation problematic: could be uds
science公布的全球最前沿的125个科学问题
science公布的全球最前沿的125个科学问题Science公布的全球最前沿的125个科学问题一、数学1. What makes prime numbers so special?什么使素数如此特别？2. Will the Navier–Stokes problem ever be solved?纳维尔-斯托克斯问题会得到解决吗？3. Is the Riemann hypothesis true?黎曼猜想是真的吗？二、化学1. Are there more color pigments to discover?还有更多色彩元素可发现吗？2. Will the periodic table ever be complete?元素周期表会完整吗？3. How can we measure interface phenomena on the microscopic level? 如何在微观层面测量界面现象？4. What is the future for energy storage？能量存储的未来是怎样的？5. Why does life require chirality?为什么生命需要手性？6. How can we better manage the world's plastic waste?我们如何更好地管理世界上的塑料废物？7. Will AI redefine the future of chemistry?AI会重新定义化学的未来吗？8. How can matter be programmed into living materials?物质如何被编码而成为生命材料？9. What drives reproduction in living systems?是什么驱动生命系统的复制？三、医学与健康1. Can we predict the next pandemic?我们可以预测下一次流行病吗？2. Will we ever find a cure for the common cold?我们会找到治疗感冒的方法吗？3. Can we design and manufacture medicines customized for individual people? 我们可以设计和制造出为个人定制的药物吗？4. Can a human tissue or organ be fully regenerated?人体组织或器官可以完全再生吗？5. How is immune homeostasis maintained and regulated?如何维持和调节免疫稳态？6.Is there a scientific basis to the Meridian System in traditional Chinese medicine?中医的经络系统有科学依据吗？7. How will the next generation of vaccines be made?下一代疫苗将如何生产？8. Can we ever overcome antibiotic resistance?我们能否克服抗生素耐药性？9. What is the etiology of autism?自闭症的病因是什么？10. What role does our microbiome play in health and disease?我们的微生物组在健康和疾病中扮演什么角色？11. Can xenotransplantation solve the shortage of donor organs?异种移植能否解决供体器官的短缺问题？四、生命科学1. What could help conservation of the oceans?什么可以帮助保护海洋？2. Can we stop ourselves from aging?我们可以阻止自己衰老吗？3. Why can only some cells become other cells?为什么只有一些细胞会变成其他细胞？4. Why are some genomes so big and others very small?为什么有些基因组非常大而另一些却很小？5. Will it be possible to cure all cancers?有可能治愈所有癌症吗？6. What genes make us uniquely human?哪些基因使我们人类与众不同？7. How do migratory animals know where they're going?迁徙动物如何知道它们要去哪里？8. How many species are there on Earth?地球上有多少物种？9. How do organisms evolve?有机体是如何进化的？10. Why did dinosaurs grow to be so big?为什么恐龙长得如此之大？11. Did ancient humans interbreed with other human-like ancestors? 远古人类是否曾与其他类人祖先杂交？12. Why do humans get so attached to dogs and cats?人类为什么会对猫狗如此着迷？13. Will the world's population keep growing indefinitely?世界人口会无限增长吗？14. Why do we stop growing?我们为什么会停止生长？15. Is de-extinction possible?能否复活灭绝生物？16. Can humans hibernate?人类可以冬眠吗？17. Where do human emotions originate?人类的情感源于何处？18. Will humans look physically different in the future?未来人类的外貌会有所不同吗？19. Why were there species explosions and mass extinction?为什么会发生物种大爆发和大灭绝？20. How might genome editing be used to cure disease?基因组编辑将如何用于治疗疾病？21. Can a cell be artificially synthesized?可以人工合成细胞吗？22. How are biomolecules organized in cells to function orderly and effectively? 细胞内的生物分子是如何组织从而有序有效发挥作用的？五、天文学1. How many dimensions are there in space?空间中有多少个维度？2. What is the shape of the universe?宇宙的形状是怎样的？3. Where did the big bang start?大爆炸从何处开始？4. Why don't the orbits of planets decay and cause them to crash into each other? 为什么行星的轨道不衰减并导致它们相互碰撞？5. When will the universe die? Will it continue to expand?宇宙何时消亡？它会继续膨胀吗？6. Is it possible to live permanently on another planet?我们有可能在另一个星球上长期居住吗？7. Why do black holes exist?为什么存在黑洞？8. What is the universe made of?宇宙是由什么构成的？9. Are we alone in the universe?我们是宇宙中唯一的生命体吗？10. What is the origin of cosmic rays?宇宙射线的起源是什么？11.What is the origin of mass?物质的起源是什么？12. What is the smallest scale of space-time?时空的最小尺度是是多少？13. Is water necessary for all life in the universe, or just on Earth?水是宇宙中所有生命所必需的么，还是仅对地球生命？14. What is preventing humans from carrying out deep-space exploration? 是什么阻止了人类进行深空探测？15. Is Einstein's general theory of relativity correct?爱因斯坦的广义相对论是正确的吗？16. How are pulsars formed?脉冲星是如何形成的？17. Is our Milky Way Galaxy special?我们的银河系特别吗？18. What is the volume, composition, and significance of the deep biosphere? 深层生物圈的规模、组成和意义是什么？19. Will humans one day have to leave the planet (or die trying)?人类有一天会不得不离开地球吗（还是会在尝试中死去）？20. Where do the heavy elements in the universe come from?宇宙中的重元素来自何处？21. Is it possible to understand the structure of compact stars and matter? 有可能了解致密恒星和物质的结构吗？22. What is the origin of the high-energy cosmic neutrinos?高能宇宙中微子的起源是什么？23. What is gravity?什么是重力？六、物理学1. Is there a diffraction limit?有衍射极限吗？2. What is the microscopic mechanism for high-temperature superconductivity?高温超导的微观机理是什么？3. What are the limits of heat transfer in matter?物质传热的极限是什么？4. What are the fundamental principles of collective motion?集体运动的基本原理是什么？5. What are the smallest building blocks of matter?什么是物质的最小组成部分？6. Will we ever travel at the speed of light?我们会以光速行驶吗？7. What is quantum uncertainty and why is it important?什么是量子不确定性，为什么它很重要？8. Will there ever be a "theory of everything"?会有“万有理论”吗？9. Why does time seem to flow in only one direction?为什么时间似乎只朝一个方向流动？10. What is dark matter?什么是暗物质？11. Can we make a real, human-size invisibility cloak?我们可以制作出真人大小的隐形斗篷吗？12.Are there any particles that behave oppositely to the properties or states of photons?是否存在与光子性质或状态相反的粒子？13. Will the Bose-Einstein condensate be widely used in the future?玻色-爱因斯坦冷凝体未来会被广泛使用吗？14. Can humans make intense lasers with incoherence comparable to sunlight? 人类能制造出与太阳光相似的非相干强激光吗？15. What is the maximum speed to which we can accelerate a particle?我们最多可以将粒子加速到多快？16.Is quantum many-body entanglement more fundamental than quantum fields?量子多体纠缠比量子场更基本吗？17. What is the optimum hardware for quantum computers?量子计算机的最佳硬件是什么？18. Can we accurately simulate the macro- and microworld?我们可以精确模拟宏观和微观世界吗？七、信息科学1. Is there an upper limit to computer processing speed?计算机处理速度是否有上限？2. Can AI replace a doctor?AI可以代替医生吗？3. Can topological quantum computing be realized?拓扑量子计算可以实现吗？4. Can DNA act as an information storage medium?DNA可以用作信息存储介质吗？八、工程与材料科学1. What is the ultimate statistical invariances of turbulence?湍流的最终统计不变性是什么？2. How can we break the current limit of energy conversion efficiencies?我们如何突破当前的能量转换效率极限？3. How can we develop manufacturing systems on Mars?我们如何在火星上开发制造系统？4. Is a future of only self-driving cars realistic?纯无人驾驶汽车的未来是否现实？九、神经科学1. What are the coding principles embedded in neuronal spike trains?神经元放电序列的编码准则是什么？2. Where does consciousness lie?意识存在于何处？3.Can human memory be stored, manipulated, and transplanted digitally?能否数字化地存储、操控和移植人类记忆？4. Why do we need sleep?为什么我们需要睡眠？5. What is addiction and how does it work?什么是成瘾？6. Why do we fall in love?为什么我们会坠入爱河？7. How did speech evolve and what parts of the brain control it?言语如何演变形成，大脑的哪些部分对其进行控制？8. How smart are nonhuman animals?除人类以外的其他动物有多聪明？9. Why are most people right-handed?为什么大多数人都是右撇子？10. Can we cure neurodegenerative diseases?我们可以治愈神经退行性疾病吗？11. Is it possible to predict the future?有可能预知未来吗？12. Can we more effectively diagnose and treat complex mental disorders?精神障碍能否有效诊断和治疗？十、生态学1. Can we stop global climate change?我们可以阻止全球气候变化吗？2. Where do we put all the excess carbon dioxide?我们能把过量的二氧化碳存到何处？3. What creates the Earth's magnetic field (and why does it move)?是什么创造了地球的磁场（为什么它会移动）？4.Will we be able to predict catastrophic weather events (tsunami, hurricanes, earthquakes) more accurately?我们是否能够更准确地预测灾害性事件（海啸、飓风、地震）？5. What happens if all the ice on the planet melts?如果地球上所有的冰融化会怎样？6. Can we create an environmentally friendly replacement for plastics?我们可以创造一种环保的塑料替代品吗？7. Can we achieve a situation where essentially every material can be recycled and reused?几乎所有材料都可以回收再利用是否可以实现？8. Will we soon see the end of monocultures like wheat, maize, rice, and soy?我们会很快看到小麦、玉米、大米和大豆等单一作物的终结吗？十一、能源科学1. Could we live in a fossil-fuel-free world?我们可以生活在一个去化石燃料的世界中吗？2. What is the future of hydrogen energy?氢能的未来是怎样的？3. Will cold fusion ever be possible?冷聚变有可能实现吗？十二、人工智能1. Will injectable, disease-fighting nanobots ever be a reality?可注射的抗病纳米机器人会成为现实吗？2. Will it be possible to create sentient robots?是否有可能创建有感知力的机器人？3. Is there a limit to human intelligence?人类智力是否有极限？4. Will artificial intelligence replace humans?人工智能会取代人类吗？5. How does group intelligence emerge?群体智能是如何出现的？6. Can robots or AIs have human creativity?机器人或AI 可以具有人类创造力吗？7.Can quantum artificial intelligence imitate the human brain?量子人工智能可以模仿人脑吗？8. Could we integrate with computers to form a human-machine hybrid species? 我们可以和计算机结合以形成人机混合物种吗？。
Temperature Dependence of the Spin Polarization of a Quantum Hall Ferromagnet
1
A rapidly growing body of evidence, both theoretical [1{3] and experimental [4{7], strongly suggests that the lowest-lying charged excitation of the spin-polarized = 1 quantum Hall state is a spin-texture called a Skyrmion. This many-body state consists of radial spin density that is reversed at the center but gradually heals to the spin background over many magnetic lengths. The spin density distribution is determined by the interplay of the ferromagnetic exchange interaction and the Zeeman energy. The exchange interaction favors large Skyrmions while the Zeeman term favors smaller excitations. In GaAs samples presently under investigation the exchange energy can be up to two orders of magnitude larger than the Zeeman energy. Hartree-Fock calculations [2] predict that Skyrmions should consist of 3 4 spin ips per unpaired ux quantum for small excursions about = 1, a result consistent with early experimental work on the lling factor ( ) dependence of the zero temperature spin polarization near = 1 [4,6]. This dominance of the exchange interaction over the Zeeman energy has led theorists to refer to the = 1 quantum Hall state as the quantum Hall ferromagnet. In GaAs heterostructures experimentalists are presented an unprecedented opportunity to probe the physics of two-dimensional electron ferromagnetism in a well-characterized system. Thus insights gained from the thermodynamics of the spin polarization will be of interest not only to those studying many-body e ects in the integral quantum Hall regime, but also more generally, may elucidate the physics of 2D electron magnetism. In this communication we report on the experimental determination of the spin polarization as a function of temperature for such a = 1 quantum Hall ferromagnet. The system consists of a single-side n-modulation doped AlGaAs-GaAs single quantum well (SQW). The well thickness is 250 with an electron density of Ns = 1:8 10 cm and mobilA ity = 2:6 10 cm =V s. In order to perform absorption measurements the samples were mounted strain-free and thinned to 0:5m. The spin polarization is monitored through band-to-band absorption spectroscopy which distinguishes the occupancy of the two electron spin states. Band-gap absorption spectra show striking temperature dependence due to changes in the occupations of the spin-split states of the ground Landau level at lling factors
关于核的英语科普作文
关于核的英语科普作文The Fascinating World of Nuclear ScienceNuclear science is a captivating field that explores the fundamental building blocks of matter - the atomic nucleus. At the heart of every atom lies a dense core composed of protons and neutrons, held together by the immensely powerful strong nuclear force. This force is so mighty that it can bind nucleons together despite the repulsive electromagnetic force between positively charged protons.Nuclear reactions, such as fission and fusion, harness the energy stored within atomic nuclei. In nuclear fission, heavy elements like uranium are split apart, releasing a tremendous amount of energy. This process powers nuclear reactors, providing us with a reliable source of electricity. On the other hand, nuclear fusion involves combining light elements, such as hydrogen, to form heavier ones, a reaction that fuels the sun and other stars.Beyond energy production, nuclear science has numerous applications in medicine, industry, and research. Radioactive isotopes are used in medical imaging and cancer treatment, while nuclear techniques are employed in materials analysis, food preservation, and even archaeology. Moreover, studying the behavior of nuclei under extreme conditions helps us unravel the mysteries of the universe, from the birth of stars to the origins of the elements we find on Earth.As we continue to explore the intriguing world of nuclear science, weunlock new possibilities and deepen our understanding of the fundamental workings of nature. With responsible research and development, nuclear science holds the potential to revolutionize our world and shape a brighter future for humanity.中文翻译：核科学是一门充满魅力的学科,它探索物质的基本组成部分——原子核。
电离杂质对载流子的散射
Ionized impurity scattering
In quantum mechanics, ionized impurity scattering is the scattering of charge carriers by ionization in the lattice.
The most primitive models can be conceptually understood as a particle responding to unbalanced local charge that arises near a crystal impurity; similar to an electron encountering an electric field. This effect is the mechanism by which doping decreases mobility.
Only when a lattice contains perfectly regular spacing can the ion-lattice interaction (scattering) lead to almost transparent behavior of the lattice. Impurity atoms in a crystal have an effect similar to thermal vibrations where conductivity has a direct relationship between temperature.
alevel p2 词汇
alevel p2 词汇**Science and Mathematics**- Atom 原子- Biology 生物学- Chemical reaction 化学反应- Circuit 电路- Data 数据- Decimal 小数- DNA 脱氧核糖核酸- Electric current 电流- Force 力- Geometry 几何学- Gravity 重力- Heart 心脏- Hypothesis 假设- Kinetic energy 动能- Laboratory 实验室- Mass 质量- Matter 物质- Maths 数学- Newton's laws of motion 牛顿运动定律- Observational study 观察性研究- Oscillation 振荡- Parallax 视差- Physics 物理学- Population 人口- Pressure 压力- Quantum 量子- Radioactivity 放射性- Resistance 电阻- Solar system 太阳系- Speed 速度- Temperature 温度- Universe 宇宙**Social Sciences and Humanities** - Anthropology 人类学- Art 艺术- Civilization 文明- Culture 文化- Democracy 民主- Economy 经济- Education 教育- Empire 帝国- Ethics 伦理学- Fiction 小说- Gender 性别- Government 政府- History 历史- Human rights 人权- Language 语言- Literature 文学- Myth 神话- Novel 小说- Philosophy 哲学- Politics 政治- Psychology 心理学- Society 社会- Slavery 奴隶制- Species 物种- Stereotype 刻板印象- Subculture 亚文化- Technology 技术**General Vocabulary**- Abundant 丰富的- Accommodation 住处；适应- Accurate 精确的- Achieve 实现- Acquire 获取- Advantage 优势- Analyse 分析- Argument 论点- Association 协会- Authentic 真正的- Calculate 计算- Categories 类别- Chronic 慢性的- Circumstance 情况- Clarify 澄清- Community 社区- Compass 指南针- Compassion 同情- Concept 概念- Concrete 具体的- Conservation 保护- Construct 建造- Context 背景- Contract 合同- Contribution 贡献- Control 控制- Convince 说服- Core 核心- Criterion 标准- Culture 文化- Cynic 愤世嫉俗者- Define 定义- Delegate 委派- Demographic 人口统计的- Determine 确定- Develop 发展- Device 设备- Distribute 分配- Diversity 多样性- Domestic 国内的- Duration 持续时间- Economy 经济- Emotion 情感- Environment 环境- Epidemic 流行病- Evident 明显的- Evaporation 蒸发- Example 例子- Explicit 明确的- Extinct 灭绝的- Factor 因素-Fade 逐渐消失- Fashion 时尚- Feature 特征- Finance 金融- Focus 焦点- Force 力量- Frequency 频率- Function 功能- Generate 产生- Global 全球的- Graph 图表- Gravity 重力- Habit 习惯-哈耶克（F.A. Hayek）-哈耶克（F.A. Hayek）-Identical 相同的- Institution 机构- Interrupt 打断- Invalidate 使无效- Inventory 清单- Issue 问题- Iterate 迭代- Judge 判断- Jury 陪审团- Kinetic 运动的- Landslide 山体滑坡- Legacy 遗产- Magnet 磁铁- Margin 边缘- Marathon 马拉松- Mass 质量- Maximise 最大化- Merge 合并- Method 方法- Misconception 误解- Modify 修改- Movement 运动- Multiply 乘以- Neutral 中性的- Novel 新颖的- Obtain 获取- Opposition 反对- Participate 参与- Pattern 模式- Phenomenon 现象- Philosophy 哲学- Pollution 污染- Population 人口- Portable 便携的- Potentially 潜在地- Poverty 贫困- Precise 精确的- Predict 预测- Preference 偏好- Prepare 准备- Presence 存在- Principle 原则- Priority 优先事项- Probability 概率- Produce 生产- Product 产品- Profile 轮廓- Propaganda 宣传- Prosperity 繁荣- Psychology 心理学- Qualify 取得资格- Quantity 数量- Questionnaire 问卷- Random 随机的- React 反应- Reflect 反映- Region 地区- Religion 宗教- Replace 替换- Representative 代表- Reservoir 水库- Restrict 限制- Revenue 收入- Sample 样本- Scarcity 稀缺性- Sector 部门- Significant 显著的- Simulate 模拟- Society 社会- Specific 具体的- Spectrum 光谱- Succeed 成功- Sufficient 足够的- Survey 调查- Symbol 符号- Target 目标- Theory 理论- Thread 线程- Transport 运输- Understand 理解- Uniform 均匀的- Utilise 利用- Validate 验证- Variable 变量- Vector 向量-Violation 违反- Vision 视力；愿景- Volunteer 志愿者这些词汇只是一部分，你可以根据具体的学科或主题进一步扩展词汇列表。
新人教版高中英语选择性必修二单词表知识点Unit 1 Science and Scientists
新人教版高中英语选择性必修二单词表知识点Unit 1 Science and ScientistsUnit 1 Science and Scientists1.cholera - ___2.___ - extremely bad or us。
harshseverely - ___ ___3.diarrhea - a n in which ___4.___ - the process of ___ something5.frustrated - ___6.once and for all - finally and conclusivelyall at once - suddenly。
___at once - immediately。
right awayonce again - one more timeonce in a while - nallyonce upon a time - a long time ago7.contradictory - ___。
conflictingbe contradictory to - be in conflict withcontrary - ___。
n。
or meaningcontradict - deny the ___。
___contradict oneself - say or do something that is ___n - a n of statements。
ideas。
or features that are opposed to one another8.n - the process of infecting or the state of being infectedinfect - ___-causing organisminfected - having been ___-causing organism9.germ - a anism。
核能工程专业英语
LESSON 1 THE BASIC CONCEPTS FOR NUCLEAR PHYSICS (4)W ORD S TUDY: (4)Word-building (4)New words: (6)R EADING C OMPREHENSION (9)R EADING C OMPREHENSION S KILL (9)Basic Reading Skill I- How to Read a Text (9)Basic Reading Skill II - Reading in Thought Groups (9)Reading Practice (10)LESSON 2 RADIATION (11)S TRUCTURE S TUDY--THE PASSIVE (11)W ORD S TUDY: (11)Synonym (11)Word-building (11)New Words (12)R EADING C OMPREHENSION S KILL (14)Reading Attack Skill--Using Context Clues for Word Meanings (14)Reading Practice (15)LESSON 3 NUCLEAR REACTION (16)W ORD S TUDY (16)OPPOSITES EXERCISE (16)WORD BUILDING (16)New Words (16)R EADING C OMPREHENSION S KILL (18)Reading for the Main Idea (18)Recognizing Important Facts or Details (18)Looking for the Topic Sentence (18)R EADING P RACTICE (19)LESSON 4 NUCLEAR MATERIAL (20)W ORD S TUDY (20)Nouns and their associated V erbs (20)Word Building (20)New Word (20)S TRUCTURE S TUDY (23)R EADING C OMPREHENSION S KILLS (23)Making Inferences While Reading (23)Reading beyond the Line (24)R EADING P RACTICE (24)LESSON 5 THE THEORY OF NUCLEAR REACTORS (25)W ORD S TUDY (25)COMPOUND NOUNS AND NOUN PHRASES (25)Word Building (26)New Words (26)R EADING C OMPREHENSION S KILL (27)Reading for Implied Meanings (27)Drawing Conclusion While Reading (27)R EADING P RACTICE (28)LESSON 6 NUCLEAR REACTOR CONCEPTS (29)W ORD S TUDY (29)Word Building (29)Phrasal (Prepositional) Verbs (29)New Words (29)R EADING C OMPREHENSION S KILL (31)Understanding Figurative Language (31)A General Review of Reading Skills (32)R EADING P RACTICE (32)LESSON 7 NUCLEAR REACTOR THERMOHYDRAULICS (33)W ORD S TUDY (33)Words with Different Meanings for the Same Function (33)Word-Building (33)New Words (34)S TRUCTURE S TUDY (36)R EADING C OMPREHENSION S KILL (36)Scanning (36)R EADING P RACTICE (37)LESSON 8: THE BOILING WATER REACTOR (38)W ORD S TUDY (38)Synonyms Exercise (38)Words With Different Functions (38)Word Building (39)New Words (39)R EADING C OMPREHENSION S KILL (41)Increasing Word Power (41)R EADING P RACTICE (41)LESSON 9 THE HEAVY-WATER-MODERATED REACTOR (45)W ORD S TUDY (45)New Words (45)R EADING C OMPREHENSION S KILL (48)Recognizing Signal Words (48)R EADING P RACTICE (49)LESSON 10 PRESSURED WATER REACTOR (52)W ORD S TUDY (52)Word-Building (52)Structural Words-Modifying Connectives (52)New Words (52)R EADING C OMPREHENSION S KILL (57)The 5 Ws (57)R EADING P RACTICE (57)LESSON 11 REACTOR VESSEL AND INTERNALS (60)W ORD S TUDY (60)New Words (60)R EADING C OMPREHENSION S KILL (62)Avoiding Vocalization and Inner Speech (62)R EADING P RACTICE (63)LESSON 12 REACTOR CORE AND FUEL (65)W ORD S TUDY (65)New Words (65)R EADING C OMPREHENSION S KILL (68)Broadening Eye Span (68)S CIENTIFIC W RITING-T YPE OF W RITING S UMMARY (69)Abstract (69)Report (70)LESSON 13 THE MAIN COMPONENTS IN PWR COOLANT SYSTEM (71)W ORD S TUDY (71)New Words (71)R EADING C OMPREHENSION S KILL (74)Skimming (74)S CIENTIFIC W RITING -T YPE OF W RITING (75)Instructions (75)Explanation (76)LESSON 14 PRESSURIZED W ATER REACTOR SYSTEMS AND CONTAINMENT (78)N EW W ORDS (78)R EADING C OMPREHENSION S KILL (82)Distinguishing Fact from Opinion (82)S CIENTIFIC W RITING --T YPE OF WRITING (82)Instruction/Hypothesizing (82)Discussion (83)LESSON 15 THE STEAM TURBINE (84)W ORD S TUDYING (84)New Words (84)R EADING C OMPREHENSION S KILL (87)Recognizing Denotation and Connotation (87)S CIENTIFIC W RITING --T YPE OF WRITING (88)Explanation (88)Informed lecture oral-explanation (89)Lesson 1 The Basic Concepts for nuclear Physics Word Study:Word-buildingTry to figure out the meaning of the new words, based on the surrounding information or the word itself.A common way of making new words in English is●by adding standard combinations of letters to existing words,●either at the beginning (prefixes)●or at the end (suffixes).By noting these carefully, you will find it is easy to make large increases in your recognition vocabulary.to act—action; to apply—applicator; to observe—observation; assign—assignment;relax—relaxation; introduce –introduction; comprehend –comprehension; concentrate—concentration.The suffix –ium (specially refer to the metal element)The prefixes in- and un (make an adjective negative/affirmative)incomplete means 'not complete'; unconnected means 'not connected'.in-:accurate; capable; direct; essential; frequent.un-:able; stable; usual; critical; reliable; successful; imaginative; true.New words:nuclei [nju:kliai] n. A plural of nucleus.nucleus n. A central or essential part around which other parts are gathered or grouped; a core:at one time adv. 同时, 曾经proton n. A stable, positively charged subatomic particle in the baryon family having a mass 1,836 times that of the electron.baryon n. Any of a family of subatomic particles, including the nucleon and hyperon multiplets, that participate in strong interactions, are composed of three quarks, and are generally more massivethan mesons.neutron n. An electrically neutral subatomic particle in the baryon family, having a mass 1,839 times that ofReading Comprehension1.What’s the structure of an atom?2.What’s the mass number? And why do we need this term?3.What’s the difference between the isotopes of same kind atom?4.How can we obtain the isotopes?5.Is the chemical attribute of isotopes different? What about the physical characteristic then?6.How to express the atomic mass in the nuclear engineering?7.What’s the Avogadro’s number?8.What’s the electron-volt? Is that a power unit?9.Why is the mass of atom not equal to the sum of the masses of its constituent particles?10.What’s the mass deficiency? And why?11.When the nucleons are very closed, what will happen? And why?12.What’s the binding energy? And how to calculate it?13.Please explain the stability of one nucleus from the binding energy’s point of view.14.How to make the nucleus excited? Is the excited status of nucleus same with the excited status of atom?15.How does the excited nucleus decay?16.What’s the fission process? Who and how find it?17.Theoretically, any nuclei can fission, but do we consider that the fissile nuclei are only 3 isotopes?18.After the fissile absorbs a neutron, what will happen?Reading Comprehension SkillBasic Reading Skill I- How to Read a TextReading with understanding depends on the interplay of three factors:●vocabulary, structure (grammar), and meaning;in other words, successful comprehension depends on one's actual command of the language. But generally a good knowledge of reading techniques or skills will not only make reading easier, but also help improve reading comprehension to a certain extent.It is advisable to read a comprehension passage at least twice:●the first time, to obtain a global impression of the text,● a second time to concentrate on the important details.●Sometimes a third reading is necessary to check items that caused difficulty.First Reading: Read the text, at your normal speed, trying to get a good idea of what the passage is about. Second Reading: Now read the passage again. This time, try to remember the important details and pay due attention to points that seem difficult. If there is a word you are not familiar with, do not waste too much time worrying about what it might mean. Just look at what comes before and after, make an intelligent guess and then go on.Basic Reading Skill II - Reading in Thought GroupsComprehension - understanding what you are reading is important; but the speed with which you read is important, too. While making constant efforts to improve your reading comprehension, you should try consciously to increase your reading speed. And to read in thought groups is an easy, yet effective, way of picking up speed and fluency.Take these two sentences:1.The little boy, Johnnie, had been up with a packet of mints, and said he wouldn't go out to play until the post hadcome.2.From the second floor flat she could see the postman when he came down the street, and the little boy from theground floor brought up her letters on the rare occasions when anything came.How to read them?1. The little boy Johnnie --had been up --with a packet of mints --and said --he wouldn't go out to play --until the post had come.2. From the second floor flat --she could see the postman –when he came own the street--and the little boy from the ground floor –brought up her letters—on the occasion—when anything came.Reading PracticeTHE SCIENTIFIC ATTITUDEWhat is the nature of the scientific attitude the attitude of the chemistry, geology, engineering, medicine or any other science?We all know that science plays an important role in the societies in which we live. Many people believe, however, that our progress depends on two different aspects of science. The first of these is the application of the machines, products and systems of applied knowledge that scientists and technologists develop. Through technology, science improves the structure of society and helps man to gain increasing control over his environment. New fibers and drugs, faster and safer means of transport, new systems of applied knowledge (psychiatry, operational research, 'etc.) are some examples of this aspect of science.The second aspect is the application by all members of society, from the government official to the ordinary citizen, of the special methods of thought and action that scientists use in their work.What are these special methods of thinking and acting? First of all, it seems that a successful scientist is full of curiosity-be wants to find out how and why the universe works. He usually directs his attention towards problems which he notices have no satisfactory explanation and his curiosity makes hint look for underlying relationships even if the data available se to be unconnected. Moreover, he thinks he can improve the existing conditions, whether of pure or applied knowledge, and enjoys to solve the problems which this involves.He is a good observer, accurate, patient and objective and applies persistent and logical thought to the observations he makes. He utilizes the facts he observes to the fullest extent. For example, trained observers obtain a very large amount of information about a star (e.g. distance, mass, velocity, size, etc.) mainly from the accurate analysis of the simple lines that appear in a spectrum.He is skeptical(skeptical)--he does not accept statements which are not based on the most completed evidence available-and therefore rejects authority as the sole basis for truth. Scientists always check statements and make experiments carefully and objectively to verify them.Furthermore, he is not only critical of the work of others, but also of his own, since he knows that man, is the least retable of scientific instruments and that a number of factors tend to disturb impartial and objective investigation.Lastly, he is highly imaginative since he often has to look for relationships in data which are not only complex but also frequently incomplete. Furthermore, he needs imagination if he wants to make hypotheses of how processes work and how events take place.These seem to be some of the ways in which a successful scientist or technologist thinks and acts.Comprehension: some sciences. two ways in which science can help society to develop.3.Give some examples of the ways in which science influences everyday life.4.What elements of science can the ordinary citizen use in order to help his society to develop?5.How can you describe a person who wants to find out how and why the universe works?6.What is the role of curiosity in the work of a scientist? some of the qualities of a good observer.8.Give an example of how observed facts are utilized to the fullest.9.How does a sceptical person act?10.to How does the scientist act towardsa)evidence presented by other people,b)evidence which he presents in his own work?11.What do you know about the data, which the scientist often has to use? How does this affect his way ofthinking?12.For what other purposes does a scientist need imagination?Lesson 2 RadiationStructure Study--THE PASSIVEWe use the passive when we have little interest in or knowledge of, the doer of the action but are more interested in what happens to, or is done to the person or thing thus affected.Note: if the doer of the action has some importance (though less than the object), or is needed to complete the sense of the sentence, it is given, e.g. 'A knowledge of statistics is required by every type of scientist.Word Study:SynonymWord-building1.The suffix –ion(-ation, -ition)This suffix forms nouns from verbs with the meaning of: process or result of doing something. Thus●'operation' means: process or result of operating.●'addition' (process or result of adding) from (to) add,●'subtraction' from subtract,●'division' from divide,●'multiplication' from multiply.●Using -ation, make nouns from the following verbs: apply; adapt; specialize; compute; calculate; isolate;combine; explain; investigate.2.The suffix -mentThis suffix forms nouns from the corresponding verbs, e.g.●'measurement' from the verb (to) measure.●By adding -ment form nouns from the following verbs: equip; move; adjust; establish; attach; improve; state.3.The suffix -ityThis suffix forms nouns from the corresponding adjectives, e.g.●'activity' from the adjective active,●'probability' from probable,●and 'simplicity' from simple.●Form nouns from the following: alkaline; relative; potential; complex; equal; reliable; acid.4.The prefix-suffix enThis is used either as a prefix to adjectives (or occasionally nouns) to form a verb (e.g. 'enable', 'enlarge', etc.) or more commonly as a suffix, e.g. 'widen' (from wide).●By adding -en, form verbs front the following: length; strength; tight; weak; loose; short; deep; height. New WordsReading Comprehension SkillReading Attack Skill--Using Context Clues for Word MeaningsWhen you read a comprehension text, you will inevitably find some words you don't know. Sometimes you take time out to look up a new word in the dictionary, but doing that too many times slows down your reading. In fact, you can often figure out meanings of new words or expressions without using the dictionary. Look at the context of each word or expression -- the sentence that the word expression is in and the sentences that come before and after. It is usually possible to find hints or clues about its definition from the context..Context Clue 1: DefinitionSometimes a writer knows that a word is unfamiliar or strange to many readers. To make the word easier tounderstand, the writer may include a definition of the word in a sentence. This context clue is the easiest one to spot.Context Clue 2: RestatementMore often, you may find a restatement, which tells you almost as much as a definition.Context Clue 3: General knowledgeMore often than not, the meaning of many words can be readily guessed if you use your own experience or general knowledge of the subject.Context Clue 4: Related informationSometimes you can make an intelligent guess of the meaning of some new words or expressions if you fit together related information from the surrounding text.When you come across a new word or expression in a comprehension passage, you are well advised to notice how the word or expression is repeated later in the text. Generally the more often it is used, the easier it is to understand.Context Clue 5: ExamplesExamples can also give you some clues or hints to the meanings of unfamiliar words.Context Clue 6: ComparisonWhen we compare things, we see how they are like each other. So comparisons in writing can give you clues to the meanings of unfamiliar words.Context Clue 7: ContrastThe use of a contrast can give you a hint to the meaning of an unfamiliar word. Sometimes a sentence tells you the negative or opposite of what a new word means.Reading PracticeNUMBERS AND MA THEMATICSIt is said that mathematics is the base of all other sciences, and that arithmetic, the science of numbers, is the base of mathematics. Numbers consist of whole numbers (integers) which are formed by the digits 0, 1, 2, 3, 4, 5 6, 7, 8 and 9 and by combinations of them. For example, 247-two hundred and forty seven is a number formed by three digits. Parts of numbers smaller than: are sometimes expressed in terms of fractions, but in scientific usage they are given as decimals. This is because it is easier to perform the various mathematical operations if decimals are used instead of fractions. The main operations are: to add, subtract, multiply and divide; to square, cube or raise to any other power; to take a square, cube or any other root and to find a ratio or proportion between pairs of numbers or a series of numbers. Thus, the decimal, or ten-scale, system is used for scientific purposes throughout the world, even in countries whose national systems of weights and measurements are based upon other scales. The other scale in general use nowadays is the binary, or two-scale, in which numbers are expressed by combinations of only two digits, 0 and 1:. Thus, in the binary scale, 2 is expressed as 010, 3 is given as 011, 4 is represented as 100, etc.This scale is perfectly adapted to the 'off-on' pulses of electricity, so it is widely used in electronic computers: because of its simplicity it is often called 'the lazy schoolboy's dream!Other branches of mathematics such as algebra and geometry are also extensively used in many sciences and even in some areas of philosophy. More specialized extensions, such as probability theory and group theory, are now applied to an increasing range of activities, front economics and the design of experiments to war and politics. Finally, a knowledge of statistics is required by every type of scientist for the analysis of data. Moreover, even an elementary knowledge of this branch of mathematics is sufficient to enable the journalist to avoid misleading his readers, or the ordinary citizen to detect the attempts which are constantly made to deceive him.Comprehension:1.What is the relationship of mathematics to the other sciences?2.What is the science of numbers called? a two-digit integer, two ways of expressing parts of the number one (unity). the common arithmetical operations. Using actual numbers, give examples of each.6. What are the two number-systems commonly used throughout the world?7. Give examples of numbers in the binary system.8. What are the advantages of each system?9.Name some other branches of mathematics. 10. What branch of mathematics is very useful to the ordinary citizen? Why? Lesson 3 Nuclear Reaction Word StudyOPPOSITES EXERCISEWORD BUILDINGThe suffix –ize , frequently spelt –ise .This forms verbs from nouns and adjectives, and has the meaning: to cause to be or have , or to subject to a process of , e.g.analogizing is equivalent to: subjecting (the problem) to a process of analogy.By adding -ize, form verbs fromthe following: standard; special; local; pressure; theory; sterile; popular;familiar; neutral; optimum.NOTE: analyze, from analysis; paralyze, from paralysis; minimize, from minimum; maximize, from maximum; and utilize, from use.In technical literature, this suffix is sometimes used with the names of persons or places associated with certain processes) e.g., macadamize (road engineering), pozzuolize (geology and engineering), and pasteurize (food technology). New WordsReading Comprehension SkillReading for the Main IdeaWhat is the most important element in any paragraph or passage? Without a doubt, it is the idea or the central idea, which gives the paragraph or passage a purpose and direction. Naturally, the first step to improve your comprehension’s to practice reading a bit faster for the main idea.When you are reading paragraphs for the main idea, try to force yourself to read a bit faster than usual. By doing so, you will find it easier to concentrate on ideas and the relationships between ideas. The slow reader usually cares too much about individual words and thus may actually comprehend less than the quick reader.In reading paragraphs, you will inevitably come across some words you don't understand. Don't waste too much time worrying about them. Just continue your reading. The most important thing is to understand the material as a whole and one or two unknown words won't make much difference.Recognizing Important Facts or DetailsTo understand the main idea thoroughly, however, you must under-stand the important facts or details which help develop or support it, These facts and details give you a deeper understanding of the main idea. They may prove a point, show a relationship between ideas, or give examples to help you understand the main idea more fully.Here are some ways to help you recognize important facts or details :1.Read for the main idea. If you have identified the main idea, you can more easily recognize the important factsthat support it.2.Keep it in mind that not all facts or details are equally important. Look only for the facts related to the mainidea.3.To check on your understanding of the material you have read, review the facts or details which you havedecided fire the most important. Then consider if they support, what you have identified as the main idea. If adding up the facts or details does not lead logically to the main idea, you have failed either to identify the main idea or to select the important supporting details.Looking for the Topic SentenceMore often than not, one sentence in a paragraph tells the reader exactly what the subject of the paragraph is and thusbriefly an idea whose full meaning and significance are developed by the supporting details. It may appear in the beginning, or in the middle, or at the end of a paragraph, or at both the beginning and end.Reading PracticeSCIENTIFIC METHOD AND THE METHODS OF SCIENCEIt is sometimes said that there is no such thing as the so-called 'scientific method'; there are only the methods used in science. Nevertheless, it seems clear that there is often a special sequence of procedures, which is involved in the establishment of the working principles of science. This sequence is as follows: (1) a problem is recognized, and as much information as appears to be relevant is collected; (2) a solution (i.e. a hypothesis) is proposed and the consequences arising out of this solution are deduced; (3) these deductions are tested by experiment, and as a result the hypothesis is accepted, modified or discarded.As an illustration of this we can consider the discovery of air-pressure. Over two thousand years ago, men discovered a method of raising water front one level to another by means of the vacuum pump. When, however, this machine passed into general use in the fifteenth and sixteenth centuries, it was discovered that, no matter how perfect the pump was, it was not possible to raise water vertically more than about 35-feet. Why?Galileo, amongst others, recognized the problem, but failed to solve it.The problem was then attacked by Torrice11i. Analogizing front the recently-discovered phenomenon of water-pressure (hydrostatic pressure), he postulated that a deep 'sea of air' surrounded the earth; it was, he thought, the pressure of this sea of air which pushed on the surface of the water and caused it to rise in the vacuum tube of a pump. A hypothesis, then, was formed. The next step was to deduce the consequences of the hypothesis. Torricelli reasoned that this 'air pressure' would be unable to push a liquid heavier than water as high as 35 feet, and that a column of mercury for example, which weighed about 14 times more than water would rise to only a fourteenth of the height of water; i.e. approximately 2.5 feet. He then tested this deduction by means of the experiment we all know, and found that the mercury column measured the height predicted. The experiment therefore supported the hypothesis. A further inference was drawn by Pascal, who reasoned that if this 'sea of air' existed, its pressure at the bottom (i.e. sea-level) would be greater than its pressure further up, and that therefore the height of the mercury column would decrease in proportion to the height above sea-level. He then carried th6 mercury tube to the top of a mountain and observed that the column fell steadily as the height increased, while another mercury column at the bottom of the mountain remained steady (an example of another of the methods of science, the controlled experiment). This further proof not only established Torrice11i's hypothesis more securely, but also demonstrated that, in some aspects, air behaved fie water; this, of course, stimulated further enquiry.Comprehension1.What does the establishment of the working laws of science often involve?2.What does a scientist collect when he tries to establish a scientific law?3.What is the next step in the process described above?4.What does the scientist then deduce?5.How does he proceed to verify these deductions?6.What does he finally do with his original hypothesis?7.Give an, approximate date for the invention of the vacuum pump.8.Is it possible to raise water from the bottom floor of a building to the roof 50 feet above, using a vacuum pump?Why?9.What was Torricelli's theory about the height of the water in a vacuum tube?10.What were his deductions concerning the effect of air pressure on a column of mercury?11.What further inference was made by Pascal?12.Why did he use two mercury tubes?13.What were the three results of Pascal's experiment?14.What do you think happened to the mercury column when it was carried down the mountain?Lesson 4 Nuclear MaterialWord StudyNouns and their associated VerbsTo use a language properly, it is important to know not only the names of things (nouns) but also the names for the actions that are associated with them (verbs): the actions are as important as the objects. Here is a list of the verbs connected with some important nouns:To obtain: evidence | knowledge | information | results;To invent | design | develop | modify: a machine | an instrument | a process | a technique;To design, plan, make | perform, conduct, carry out | control | time | repeat: an experiment;To develop | suggest | prove, validate | disprove | modify |discard |support |put forward | test: a theory | a hypothesis. Word BuildingThe suffix –alThis forms adjectives from the corresponding nouns, e.g. 'practical' from practice, 'theoretical' from theory.Adjectives from the names of sciences ending in-ics also take this suffix, e.g. mathematics-mathematical.NOTE:theory-theoretical; geometry-geometrical; hypothesis-hypothetical; technique-technical; machine-mechanical; center-central; air-aerial; cycle-cyclical.●Form further adjective from the following: addition; condition; experiment; nature; neuter; operation; section;region; analysis; matter.The prefix inter-This is added to verbs and derivatives to give the extra meaning of: between, among, one with the other, e.g. interconnection, interaction.●Form adjectives from the following: dependent; related; national.●Form verbs from the following, using the prefix inter- in all cases : act; breed; change; connect.New Word。
临界形核功英语
临界形核功英语In the realm of nuclear physics, the concept of critical mass is pivotal to the understanding and harnessing of nuclear energy. This term refers to the smallest amount of fissile material needed for a sustained nuclear chain reaction. The chain reaction is a series of reactions in which a reactive product or by-product causes additional reactions to take place. In a nuclear reactor, the critical mass is the amount of fissile material—such as uranium-235 or plutonium-239—required to maintain a self-sustaining nuclear fission reaction.The science behind critical mass is governed by neutron kinetics and the geometry of the nuclear fuel. When a nucleus of fissile material captures a neutron, it may undergo fission, splitting into two smaller nuclei and releasing a certain amount of energy, along with more neutrons. If these neutrons are captured by other fissile nuclei, they can cause more fissions, leading to a chain reaction. However, if the mass of the fissile material is below the critical mass, the reaction will not be self-sustaining, as too many neutrons escape without causing further fissions.The concept of critical mass is not only fundamental to the operation of nuclear reactors but also to the design of nuclear weapons. In the latter, the objective is to bring a sub-critical mass to a supercritical state very quickly, usually by using conventional explosives to compress the fissile material, so that a violent and uncontrolled chain reaction occurs, releasing a massive amount of energy in a very short time.The energy released during fission comes from the slight difference in mass between the reactants and products, described by Einstein's famous equation $$E=mc^2$$, where \(E\) is energy, \(m\) is mass, and \(c\) is the speed of light. This equation shows that even a small amount of mass can be converted into a large amount of energy, which is the principle that makes nuclear energy so potent.In nuclear power plants, the critical mass is carefully controlled to ensure a steady production of energy. Control rods made of materials that absorb neutrons, such as boronor cadmium, are inserted into the reactor core to control the rate of the reaction. By adjusting the position of these rods, operators can maintain the reactor at criticality, allowing for a controlled release of energy for electricity generation.The pursuit of nuclear energy has been driven by its potential to provide a significant source of power without the carbon emissions associated with fossil fuels. However, the risks associated with nuclear power, such as the potential for accidents or the challenge of managing nuclear waste, have led to a complex debate about its role in the future energy landscape.In conclusion, the concept of critical mass is a cornerstone of nuclear physics, enabling both the destructive power of nuclear weapons and the constructive potential of nuclear energy. As society continues to grapple with the implications of nuclear technology, the principles underlying critical mass will remain at the heart of discussions about energy, security, and the environment. The ongoing research and development in nuclear science aim to improve the safety and efficiency of nuclear reactors, potentially leading to a future where nuclear energy can be harnessed with minimal risk and maximum benefit. 。
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a r X i v :0704.1642v 2 [c o n d -m a t .s t r -e l ] 20 A p r 2007Collective excitations of hard-core Bosons at half filling on square and triangularlattices:Development of roton minima and collapse of roton gapTyler Bryant and Rajiv R.P.SinghDepartment of Physics,University of California,Davis,CA 95616,USA(Dated:February 1,2008)We study ground state properties and excitation spectra for hard-core Bosons on square and tri-angular lattices,at half filling,using series expansion methods.Nearest-neighbor repulsion between the Bosons leads to the development of short-range density order at the antiferromagnetic wavevec-tor,and simultaneously a roton minima in the density excitation spectra.On the square-lattice,the model maps on to the well studied XXZ model,and the roton gap collapses to zero precisely at the Heisenberg symmetry point,leading to the well known spectra for the Heisenberg antiferromagnet.On the triangular-lattice,the collapse of the roton gap signals the onset of the supersolid phase.Our results suggest that the transition from the superfluid to the supersolid phase maybe weakly first order.We also find several features in the density of states,including two-peaks and a sharp discontinuity,which maybe observable in experimental realization of such systems.PACS numbers:I.INTRODUCTIONA microscopic theory for rotons in the excitation spec-tra of superfluids was first developed by Feynman,where he showed that the roton minima was related to a peak in the static structure factor.1This study has had broad impact in condensed matter physics ranging from Quantum Hall Effect 2to frustrated antiferromagnets.3,4,5In recent years considerable interest has also centered on Supersolid phases of matter.6While the existence of such homogeneous bulk phases in Helium remains controversial,7,8in case of lattice models such phases have been clearly established.One such example is that of hard-core Bosons hopping on a triangular-lattice,where a large enough nearest-neighbor repulsion leads to su-persolid order.9,10,11,12,13,14The nature of the excitation spectra in the superfluid phase and on approach to the supersolid transition has not been addressed for the spin-half model.Here we use series expansion methods to study the ground state properties and excitation spectra of hard-core Bosons,at half filling,on square and triangular lat-tices,with nearest neighbor repulsion.On the square-lattice,the model is equivalent to the antiferromagnetic XXZ model,and we present the elementary excitation spectra for the XXZ model with XY type anisotropy.To our knowledge this calculation has not been done before.It should be useful for experimental studies of antiferro-magnetic materials with XY anisotropy.We set the XY coupling to unity and study the spectra as a function of the Ising coupling J z .For the XY model,the spectra is gapless at q =0(the Goldstone mode of the superfluid)and has a maximum at the antiferromagnetic wavevector (π,π).As the Ising coupling is increased a roton minima develops at the antiferromagnetic wavevector,which goes to zero at the point of Heisenberg symmetry (J z =1),as expected for the system with doubled unit cell.For the triangular-lattice,the hard-core Boson model maps onto a ferromagnetic XY model,which is unfrus-trated.The nearest-neighbor repulsion,on the other hand corresponds to an antiferromagnetic Ising coupling,which is frustrated.This model cannot be mapped onto an antiferromagnetic XXZ model on the triangular lat-tice.For this model,we calculate the equal-time struc-ture factor S (q )as well as the excitation spectra,ω(q ).Once again,we find that in the absence of nearest-neighbor repulsion,the excitation spectra is gapless at q =0and has a maximum at the antiferromagnetic wavevector ((4π/3,0)and equivalent points).As the re-pulsion is increased,a pronounced peak develops in S (q )at these wavevectors and simultaneously a sharp roton minima develops in the spectra.Series extrapolations suggest that the roton gap vanishes when the repulsion term (J z )reaches a value of ≈4.5.However,we are un-able to estimate any critical exponents for the vanishing of the gap or for the divergence of the structure factor.A comparison of our structure factor data with the Quan-tum Monte Carlo data of Wessel and Troyer,leads us to suggest that the transition to the supersolid phase maybe weakly first order and occurs for a value of J z slightly less than 4.5.Our calculations also show a near minimum and flat re-gions in the spectra at the wavevectors (π,π/√2 tically or by driving the system out of equilibrium.Ameasurement of the energies associated with the charac-teristic features in the density of states can be used toaccurately determine the microscopic parameters of thesystem.II.METHODThe linked-cluster series expansions performed here in-volve writing the Hamiltonian of interest asH=H0+λH1(1)where the eigenstates of H0define the basis to be usedand H1is the perturbation to be applied in a linked clus-ter expansion.Ground state properties are then obtainedas a power series inλusing Raleigh-Schrodinger pertur-bation theory.Excited state properties are obtained following the pro-cedure outlined in22,in which a similarity transformationis obtained in order to block diagonalize the Hamiltonianwhere the ground state sits in a block by itself and theone-particle states form another block.H eff=S−1HS(2)where H effis an effective Hamiltonian for the stateswhich are the perturbatively constructed extensions ofthe single spin-flip states.The effective Hamiltonianis then used to obtain a set of transition amplitudesr=0λr c r,m,n that describe propagation of the excita-tion through a distance(mˆx+nˆy)for the square latticeand(132q x)cos(n√2q y)+cos(√4q y)cos(m−3n3(m−n)4q x) /3for the triangular lattice.In order to access values of the expansion parameterλup to and includingλ=1,we use standardfirst orderintegrated differential approximants18(IDAs)of the formQ L(x)d f3/2)(∆FIG.1:(Color online)The spin-wave dispersion of the XXZmodel on the square lattice for various values of J⊥(J z=1).The error bars give an indication of the spread of variousIDAs.The lines around the gapless points for J⊥=1showthe calculated spin-wave velocity.where J⊥=1.Now,a new series is obtained for eachvalue of J z,and the XXZ model is only obtained uponextrapolation toλ=1.In contrast to thefirst type ofexpansion,H1does not conserve total S z,and so the entire Hilbert space must be used,limiting the order ofcomputation of the series toλ10(11sites).Fig.2shows the results of the spin-wave dispersionanalysis for several values of J z from the XY model (J z=0)to the Heisenberg model(J⊥=1).Wefind that for the pure XY model,there is gapless excitationsat q=0(Goldstone modes of the superfluid phase), but there is no roton minima at the antiferromegnetic wavevector.As J z is increased,the spin-wave veloc-ity increases and a clear roton-minima develops at the antiferromagnetic wavevector.This minima collapses to zero as the Heisenberg point is approached.In fact,the doubling of the unit cell implies that for the Heisenberg limit,the spectra at q and at q+(π,π)become identi-cal.Another point of interest is that along the direction (π,0)to(π/2,π/2),which corresponds to the antiferro-magnetic zone boundary,the dispersion is veryflat for the pure XY model.A weak minimum develops at(π,0) as the Heisenberg symmetry point is reached.These re-sults should be useful in comparing with spectra of two-dimensional antiferromagnets,where there is significant exchange anisotropy.IV.TRIANGULAR LATTICEThere has been much recent interest in the XXZ model on the triangular lattice.The spin-1n M for J z=0-5.000000e-01-4.166667e-02-4.282407e-03-1.251190e-03-5.538567e-04-2.990401e-04-1.823004e-04-1.015895e-04bor repulsion.H b=−t <i,j>(b†i b j+b i b†j)+V <i,j>n i n j(9)where b†i is the bosonic creation operator,n i=b†i b i.The parameters are related by t=−J⊥/2and V=J z.For the rest of this section,we let J⊥=−1,and so V/t=−2J z/J⊥=2J z.We will continue to use the spin language as it is natu-ral for our study.For J z=0,the ferromagnetic in-plane coupling is unfrustrated.As J z is increased,the com-peting interaction leads to an emergence of a supersolid order.We have performed expansions for the triangular lat-tice XXZ model of the formH0=− <i,j>S x i S x jH1= <i,j>(−S y i S y j+J z S z i S z j)(10) where J⊥=−1.Series are obtained for each value of4J z ,and the XXZ model is obtained upon extrapolation to λ=1.The static structure factorS (k )=re i k ·r S z 0S zr (11)is shown in Fig.3along contours shown in Fig. 4.As J z increases,a peak forms at wavevector q =(4π/3,0).A plot of this point is shown in fig.5along with QMC data from Wessel and Troyer.10(0,π/31/2(π,π/31/2(4π/3,0(2π/3,0(2π/3,2π/31/2(0,0(π,π/31/2(π,0SFIG.3:(Color online)The static structure factor of the XXZ model on the triangular lattice for various values of J z (J ⊥=−1).The error bars give an indication of the spread of IDAs.2π/31/2-2π/31/24π/32π/30-2π/3-4π/3FIG.4:The hexagonal first Brillouin zone of the triangu-lar lattice and the path ABOCPQBE along which the static structure factor and spin-wave dispersion have been plotted in Figs.3and 6.1 2 3 4 5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5S (Q )J zSeries 12x1224x2436x36FIG.5:(Color online)The static structure factor at q =(4π/3,0)of the XXZ model on the triangular lattice ver-sus J z (J ⊥=−1).The error bars for the series data give an indication of the spread of IDAs.Also shown are QMC data for 12x12,24x24,and 36x36site clusters from Wessel and Troyer.10Fig.6shows the results of the spin-wave dispersion analysis for various values of J z (J ⊥=−1).The error bars give an indication of the spread of IDAs.The lines around the gapless points show the calculated spin-wave velocities.One can see the development of minima at Q with increasing J z ,with the gap completely closing at J z ∼4.5.Since IDAs are not accurate near the gapless point (q =0),the dotted line shows the estimated spin-wave velocities.We have been unable to get any consistent estimates for the critical exponents characterizing the divergence of the antiferromagnetic structure factor and the van-ishing of the roton gap as the supersolid phase is ap-proached.Furthermore,the comparison with the QMC data of Wessel and Troyer show that the QMC data begin to show deviations from our series expansion results be-fore J z =4.5.We believe,this implies that the superfluid to supersolid transition is weakly first order.Wessel and Troyer estimate the transition to be at J z ≈4.3±0.2(|t/V |=0.115±0.005).Note that the spin-wave the-ory gives the transition point to be at J z =2,9so that quantum fluctuations play a substantial role here.Addi-tional QMC studies,should provide further insight into the nature of the transition.24The calculations also show that near the midpoint of the faces of the Brillouin Zone (point B in Fig.4),the dis-persion is a minima in the direction perpendicular to the zone face QB and is very flat in other directions.This be-havior is reminiscent of the dispersion in the Heisenberg antiferromagnet on the traingular lattice where there is a true minimum at this point.4,5Note that this behav-ior is unrelated to any peak in the static structure factor and thus,as in case of the Heisenberg model,is more quantum mechanical in nature.In Fig.7,we show the density of states for the spectra5for J z =2.There are several distinguishing features in the density of states.First the largest peak in the density of states occurs close to the highest excitation energies.This is not unlike what is found in many other antiferromegnets.However,here,there is a second peak that corresponds to the flat regions in the spectra near the point B.Finally,at the roton energy there is a sharp drop in the density of states.The only contributions to the density of states below the roton gap comes from the Goldstone modes near q =0.Since the latter have very small density of states,there is a discontinuity in the density of states at the roton energy.(0,π/31/2(π,π/31/2(4π/3,0(2π/3,0(2π/3,2π/31/2(0,0(π,π/31/2(π,0∆FIG.6:(Color online)The spin-wave dispersion of the XXZ model on the triangular lattice for various values of J z (J ⊥=−1).The error bars give an indication of the spread of IDAs.The lines around the gapless points show the calculated spin-wave velocities.0 0.2 0.40.6 0.8 1D O S (a r b i t r a r y u n i t s )εFIG.7:The density of states for the XXZ model on the tri-angular lattice for J z =2(J ⊥=−1).V.SUMMARY AND CONCLUSIONSIn this paper,we have studied the excitation spectra of hard-core Boson models at half-filling on square and tri-angular lattices.The calculations show the development of the roton minima at the antiferromagnetic wavevector,due to nearest-neighbor repulsion.In accord with Feyn-man’s ideas,the development of the minima is correlated with the emergence of a sharp peak in the static structure factor.The case of triangular-lattice is clearly more in-teresting as one has a phase transition from a superfluid to a supersolid phase,where the roton gap goes to zero.Our series results suggest that the roton-gap vanishes at J z ≈4.5.However,there maybe a weakly first order transition slightly before this J z value.A more careful finite-size scaling analysis of the QMC data should pro-vide further insight into this issue.Our results of the spectra suggest two peaks in the density of states and a sharp drop in the density of states at the energy of the roton minima.If such a hard-core Boson system on a triangular-lattice is realized in cold-atom experiments,a measurement of the two peaks in the density of states and the roton minima can be used to determine independently the hopping parameter t and the nearest-neighbor repulsion V .AcknowledgmentsThis research is supported in part by the National Sci-ence Foundation Grant Number DMR-0240918.We are greatful to Stefan Wessel for providing us with the QMC data for the structure factors and to Marcos Rigol and Stefan Wessel for discussions.61R.P.Feynman,Phys.Rev.94,262(1954).2S.M.Girvin,A.H.MacDonald,and P.M.Platzman Phys.Rev.Lett.54,581-583(1985).3P.Chandra,P.Coleman and rkin,J.Phys.Cond.Matter2,7933(1990).4W.Zheng,et al,Phys.Rev.Lett.96,057201(2006);Phys.Rev.B74,224420(2006).5O.A.Starykh,A.V.Chubukov and A.G.Abanov,Phys Rev.B74,180403(2006); A.L.Chernyshev and M.E.Zhitomirsky,Phys.Rev.Lett.97,207202(2006).6E.Kim and M.H.W.Chan,Nature427,225(2004).7See for example M.Boninsegni et al,Phys.Rev.Lett.97, 080401(2006).8P.W.Anderson,W.F.Brinkman,D.A.Huse,Science 310,1164(2005).9G.Murthy,D.Arovas,and A.Auerbach,Phys.Rev.B, 55,3104(1997).10S.Wessel and M.Troyer,Phys.Rev.Lett.95,127205 (2005).11D.Heidarian and K.Damle,Phys.Rev.Lett.95,127206 (2005).12R.G.Melko, A.Paramekanti, A.A.Burkov, A.Vish-wanath,D.N.Sheng,and L.Balents Phys.Rev.Lett.95, 127207(2005).13M.Boninsegni and N.Prokof’ev Phys.Rev.Lett.95,237204(2005).14E.Zhao and Arun 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r,m,n(3,2,1)-7.291667e-02(9,5,2)-1.334928e-03(2,0,0)-4.166667e-02(4,4,0)-2.712674e-03(7,2,1)-8.897152e-03(9,5,4)-3.993759e-04(6,0,0)-5.390283e-03(8,4,0)-1.932294e-03(4,2,2)-1.627604e-02(8,6,0)-3.216877e-04(1,1,0)-1.000000e+00(7,4,1)-4.614353e-03(8,2,2)-2.558526e-03(9,6,1)-6.801940e-04(5,1,0) 1.811921e-02(6,4,2)-3.468926e-03(5,3,0)-7.265535e-03(9,6,3)-2.662506e-04(9,1,0) 4.056254e-03(7,4,3)-1.901715e-03(9,3,0)-1.895272e-03(9,7,0)-1.043517e-04(4,1,1)-2.314815e-02(8,4,4)-4.516145e-04(6,3,1)-1.033207e-02(9,7,2)-1.141074e-04(8,1,1)-1.566143e-03(7,5,0)-1.004891e-03(5,3,2)-1.060655e-02(9,8,1)-2.852685e-05(4,2,0)-3.067130e-02(6,5,1)-1.387570e-03(9,3,2)-3.716341e-03(8,2,0)-3.989385e-03(7,5,2)-1.141029e-03TABLE III:Series coefficients for the ground state energy per site E0/N and ME0/N for J z=0E0/N for J z=1E0/N for J z=20-2.500000e-01-2.500000e-01-2.500000e-0110.000000e+000.000000e+0027.500000e-03 3.000000e-02 6.750000e-023 3.000000e-03-2.700000e-024 1.989902e-03 3.271769e-03 3.263208e-025 1.356060e-03-4.706087e-026 1.018008e-03 2.253907e-037.245005e-0277.975125e-04-1.117528e-018 6.468307e-04 1.498661e-03 1.839365e-019 5.380214e-04-3.025679e-0110 4.565960e-04 1.029273e-03 5.141882e-0111 3.937734e-04-8.849178e-0112 3.441169e-047.779323e-04 1.545967e+008 TABLE IV:Series coefficients for the magnon dispersion on the triangular lattice J z=0,J⊥=−1,nonzero coefficients up to r=9are listed for compactness(the complete series can be found in Ref.23)(r,m,n)c r,m,n(r,m,n)c r,m,n(6,5,1)-6.186994e-03(9,10,6)-3.135408e-05(2,0,0)-3.125000e-02(6,8,0)-2.496675e-03(8,5,1)-3.031857e-03(6,11,1)-9.073618e-05(4,0,0)-5.786823e-03(8,8,0)-1.849982e-03(4,5,3)-3.466797e-03(8,11,1)-3.828143e-04(6,0,0)-2.263644e-03(5,8,2)-1.098718e-03(6,5,3)-3.723124e-03(7,11,3)-7.642054e-05(8,0,0)-1.158308e-03(7,8,2)-1.579331e-03(8,5,3)-2.305863e-03(9,11,3)-2.316277e-04(1,2,0)-1.500000e+00(9,8,2)-1.241335e-03(3,6,0)-7.265625e-03(9,11,5)-4.925111e-05(3,2,0) 2.236979e-02(7,8,4)-4.458355e-04(5,6,0)-7.839022e-03(6,12,0)-1.512270e-05(5,2,0) 6.223272e-03(9,8,4)-5.861054e-04(7,6,0)-3.834575e-03(8,12,0)-1.917140e-04(7,2,0) 2.729869e-03(8,8,6)-6.113630e-05(9,6,0)-2.110041e-03(7,12,2)-4.585233e-05(9,2,0) 1.431100e-03(5,9,1)-5.493588e-04(5,6,2)-5.161886e-03(9,12,2)-1.836224e-04(3,3,1)-5.677083e-02(7,9,1)-1.233659e-03(7,6,2)-3.218811e-03(9,12,4)-5.685542e-05(5,3,1)-1.275959e-02(9,9,1)-1.066119e-03(9,6,2)-1.905072e-03(7,13,1)-1.528411e-05(7,3,1)-4.959005e-03(7,9,3)-5.232866e-04(6,6,4)-1.094328e-03(9,13,1)-1.121505e-04(9,3,1)-2.443109e-03(9,9,3)-6.426095e-04(8,6,4)-1.182811e-03(9,13,3)-4.925111e-05(3,4,0)-4.916667e-02(8,9,5)-1.209317e-04(4,7,1)-3.466797e-03(7,14,0)-2.183444e-06(5,4,0)-1.289340e-02(8,9,7)-2.607109e-06(6,7,1)-3.723124e-03(9,14,0)-4.937808e-05(7,4,0)-5.280757e-03(5,10,0)-1.098718e-04(8,7,1)-2.305863e-03(9,14,2)-3.135408e-05(9,4,0)-2.735539e-03(7,10,0)-7.110879e-04(5,7,3)-1.098718e-03(8,15,1)-2.607109e-06(4,4,2)-1.596136e-02(9,10,0)-7.669912e-04(7,7,3)-1.579331e-03(9,15,3)-4.193665e-06(6,4,2)-6.186994e-03(7,10,2)-4.458355e-04(9,7,3)-1.241335e-03(9,16,0)-3.685726e-06(8,4,2)-3.031857e-03(9,10,2)-5.861054e-04(7,7,5)-2.637766e-04(9,17,1)-4.493212e-07(3,5,1)-2.179687e-02(8,10,4)-1.651312e-04(9,7,5)-4.387479e-04(5,5,1)-9.470639e-03(8,10,6)-9.124881e-069 TABLE V:Series coefficients for the magnon dispersion on the triangular lattice J z=1,J⊥=−1,nonzero coefficients up to r=9are listed for compactness(the complete series can be found in Ref.23)(r,m,n)c r,m,n(r,m,n)c r,m,n(8,4,2) 1.641818e-02(6,10,2)-1.174079e-03(2,0,0)-1.250000e-01(6,7,5)-4.696316e-04(6,5,1)-2.266297e-02(8,10,4)-1.051498e-03(6,0,0)-3.747008e-02(4,8,0)-3.632812e-03(4,5,3)-1.453125e-02(6,11,1)-4.696316e-04(2,2,0)-1.000000e-00(8,8,0)-2.634458e-03(8,5,3)-1.306500e-05(8,11,3)-1.051498e-03(6,2,0)-1.478629e-01(8,8,2)-3.898852e-03(6,6,0)-2.107435e-02(6,12,0)-7.827194e-05(2,3,1)-7.500000e-01(8,8,4)-2.957178e-03(4,6,2)-2.179687e-02(8,12,2)-7.614846e-04(6,3,1)-7.198726e-02(6,9,1)-5.919357e-03(8,6,2) 1.136255e-03(8,13,1)-3.787294e-04(2,4,0)-3.750000e-01(6,9,3)-1.565439e-03(8,6,4)-4.075885e-03(8,14,0)-1.146580e-04(6,4,0)-4.667627e-02(8,9,5)-7.614846e-04(6,7,1)-1.709052e-02(8,15,1)-1.576831e-05(4,4,2)-7.072545e-02(6,10,0)-2.499303e-03(6,7,3)-8.548979e-0310 TABLE VI:Series coefficients for the magnon dispersion on the triangular lattice J z=2,J⊥=−1,nonzero coefficients up to r=9are listed for compactness(the complete series can be found in Ref.23)(r,m,n)c r,m,n(r,m,n)c r,m,n(6,5,1)-5.113269e-01(9,10,6) 3.094665e-02(2,0,0)-2.812500e-01(6,8,0)-2.789923e-01(8,5,1)-5.927875e-01(6,11,1)-1.020493e-02(4,0,0) 3.427127e-01(8,8,0)-5.937472e-01(4,5,3)-9.659180e-02(8,11,1)-1.791293e-01(6,0,0)-3.138557e-01(5,8,2) 5.215530e-02(6,5,3)-3.793451e-01(7,11,3) 1.646341e-02(8,0,0) 2.679692e-01(7,8,2) 3.088576e-01(8,5,3)-6.470161e-01(9,11,3) 2.165711e-01(1,2,0) 1.500000e+00(9,8,2)8.731811e-01(3,6,0) 6.539063e-02(9,11,5) 4.893766e-02(3,2,0)-2.013281e-01(7,8,4)9.867811e-02(5,6,0) 3.819521e-01(6,12,0)-1.700822e-03(5,2,0) 3.245835e-01(9,8,4) 4.867085e-01(7,6,0) 4.227344e-01(8,12,0)-9.194406e-02(7,2,0)-1.324972e+00(8,8,6)-2.934241e-02(9,6,0) 1.561357e+00(7,12,2)9.878045e-03(9,2,0) 1.998149e+00(5,9,1) 2.607765e-02(5,6,2) 2.496909e-01(9,12,2) 1.748291e-01(3,3,1) 5.109375e-01(7,9,1) 2.546730e-01(7,6,2) 4.542205e-01(9,12,4) 5.664036e-02(5,3,1) 4.631412e-01(9,9,1)7.791699e-01(9,6,2) 1.278006e+00(7,13,1) 3.292682e-03(7,3,1)-2.673657e-01(7,9,3) 1.163420e-01(6,6,4)-1.264872e-01(9,13,1) 1.091019e-01(9,3,1) 2.292894e+00(9,9,3) 5.242482e-01(8,6,4)-4.585226e-01(9,13,3) 4.893766e-02(3,4,0) 4.425000e-01(8,9,5)-5.858223e-02(4,7,1)-9.659180e-02(7,14,0) 4.703831e-04(5,4,0) 5.419257e-01(8,9,7)-1.231232e-03(6,7,1)-3.793451e-01(9,14,0) 4.854225e-02(7,4,0) 3.675761e-02(5,10,0) 5.215530e-03(8,7,1)-6.470161e-01(9,14,2) 3.094665e-02(9,4,0) 2.293150e+00(7,10,0) 1.541458e-01(5,7,3) 5.215530e-02(8,15,1)-1.231232e-03(4,4,2)-4.619167e-01(9,10,0) 6.055844e-01(7,7,3) 3.088576e-01(9,15,3) 4.043528e-03(6,4,2)-5.113269e-01(7,10,2)9.867811e-02(9,7,3)8.731811e-01(9,16,0) 3.577909e-03(8,4,2)-5.927875e-01(9,10,2) 4.867085e-01(7,7,5) 5.778696e-02(9,17,1) 4.332352e-04(3,5,1) 1.961719e-01(8,10,4)-8.048695e-02(9,7,5) 3.824414e-01(5,5,1) 4.570889e-01(8,10,6)-4.309313e-03。