Dynamical mass generation in quantum field theory some methods with application to the Gro

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量子力学-薛定谔方程

Lecture 10-11Schrödinger(薛定谔)equationsPrior to 1925 quantum physics was a “hodgepodge” of hypotheses, principles, theorems and recipes . It was not a logically consistent theory.Once we know this wavefunction we know “everything” about the system!Part 1Dynamic EquationsIf we know the forces acting upon the particle than,according to classical physics , we know everything about a particle at any moment in the future.22,(),()d r F ma F U r U r m dt ==-∇-∇=r r r r r r r r22221()()0E r E r c t∂∇-=∂r r r r A differential equation by itself does not fully determine theunknown function ()(,)r t or E r t r r r .Part 2Dynamic Equation of Wave function---- Schrödinger equations用21()sin cos 2x kx kx ψ⎡⎤=+⎢⎥⎣⎦描述的粒子，只能有5种动量取值，分别是0,2,2,,k k k k -- ，对应的几率分别是11111,,,,28888，这些几率总和应该为1。

()()1111111()0220,2888811111()128888ki i i k i i p P p p k k k k P p ====⋅+⋅+-⋅+⋅+-⋅==++++=∑∑h h h h 1212(),()1(),()1(),()1k ki i i i i x P x x P x x p x xd x x p x dx x x xd x x d ψψ=======⇒=∑∑⎰⎰⎰⎰¡¡¡¡Do we have the same recipe for calculation of average momentum by using wave function in position representation? Yes, of course, we have!To find the expectation (average) value of p , we first need to represent p in terms of x and t . Consider the derivative of the wave function of a free particle with respect to x:0001(,)exp ()p i x t p x E t ⎡⎤ψ=-⎢⎥⎣⎦h We find that0000000000**000(,)(,)(,)(,)(,)()(,)(,)(,)(0)δ∂ψ=ψ⇒ψ=ψ∂∂==ψ-ψ=ψψ=∂∂-∂⎰⎰p p p p p p p p i x t p x t x t p x t x p p x t i x t dx p x t x t dx i xp x　h h h This suggests we define the momentum operator asThe expectation value of the momentum is20022220221()sin cos 2()()()()()=()()()()()ψϕϕϕϕϕ------⎡⎤=+⎢⎥⎣⎦=--++--++k k k k k k k k k k k k x kx kx C x C x C x C x C x x x x x x h h h h h h h h h h h h1()px i p x e ϕ=h ()()111111()022028888===⋅+⋅+-⋅+⋅+-⋅=∑ki i i p P p p k k k k h h h h So,we can not have definite values for the dynamical variables, such as the momentum, when the state of a particle is determined by the wave function with respect to x. We have to find the other way to describe thedynamical variables in Quantum Mechanics.For every dynamical variable or any observable thereis a corresponding Quantum Mechanical OperatorPhysical Quantities →OperatorsOperators are important in quantum mechanics. All observables have corresponding operators.Operators ↔Symbols for mathematical operation✧ The position x is its own operator ˆxx =. Done. Other operators are simpler and just involve multiplication 22x x x x ∧==⋅. ✧ The potential energy operator is just multiplication by V(x).✧ The momentum operator is defined as ˆp i x ∂=-∂h00000002211ˆˆˆˆ1()()[11ˆ(()](())()222ˆ()()())ˆ()()1ˆ()2pp xipp x p xp xix x piix px p pp xix p pp p ppx eipip x i e p eexp x p xx xpT x p p x p p x xpxx eT x T xϕϕϕϕμμμϕϕϕϕϕϕϕμϕ=====⎛⎫∂-=-==⎪∂⎝⎭===hh hhhhh()px xϕ=h000000001(,)exp()1ˆ(,)exp()(,)ˆ(,)(,)pp pp pix t p x E ti iEE x t i p x E t i x ttE x t E x t⎡⎤ψ=-⎢⎥⎣⎦∂⎧⎫⎡⎤⎛⎫ψ=-=ψ-⎬ ⎪⎢⎥∂⎝⎭⎣⎦⎭ψ=ψhh hh h Eigenvalue equation of an operatoreigenvalueDeriving the Schrödinger Equation using operators: This was a plausibility argument, not a derivation. We believe the Schrödinger equation not because of this argument, but because its predictions agree withexperiments.Schrödinger EquationNotes:The Schrödinger Equation is THE fundamental equation of Quantum Mechanics.There are limits to its validity. In this form it applies only to a single, non-relativistic particle (i.e. one withnon-zero rest mass and speed much less than c.)●On the left hand picture 13 velocity vectors of an individual fly are shown; the chain●On the right hand picture the same 13velocity vectors are assigned to 1 fly each todemonstrate that the ensemble average yields the same result, i.e. <v e> = 0,provided that each and every fly does the same thing on average.●i.e. time average = ensemble average. The new subscripts "e" and "r" denote ensemble and space, respectively. This is a simple version of a very far reaching concept in stochastic physics known under the catch word "ergodic hypothesis".●As long as every fly does - on average - the same thing, the vector average overtime of the ensemble is identical to that of an individual fly - if we sum up a fewthousand vectors for one fly, or a few million for lots of flies does not make anydifference. However, we also may obtain this average in a different way:●We do not average one fly in time obtaining <v i>t , but at any given time all flies inspace.●This means, we just add up the velocity vectors of all flies at some moment in timeand obtain <v e>r , the ensemble average. It is evident (but not easy to prove for general cases) thata) Schrödinger equation is a linear homogeneous partialdifferential equation.b) The Schrödinger equation contains the complex number i.Therefore its solutions are essentially complex (unlikeclassical waves, where the use of complex numbers isjust a mathematical convenience.)c) The wave equation has infinite number of solutions,someof which do not correspond to any physical or chemical reality.1. For an electron bound to an atom/molecule, the wavefunction must be everywhere finite, and it must vanish in the boundaries2. Single valued3. Continuous4. Gradient (dψ/dr) must be continuous5. ψψ*dτ is finite, so that ψ can be normalizedd) Solutions that do not satisfy these properties(above)DONOT generally correspond to physicallyrealizable circumstances.e) Conditions on the wave function(波函数的三个基本条件——有限、单值、连续)1. In order to avoid infinite probabilities, the wave functionmust be finite everywhere.2. The wave function must be single valued.3. The wave function must be twice differentiable. Thismeans that it and its derivative must be continuous. (An exception to this rule occurs when V is infinite.)4. In order to normalize a wave function, it must approachzero as x approaches infinity.f) Only the physically measurable quantities must be real.These include the probability, momentum and energy.Can think of the LHS of the Schrödinger equation as a differentialoperator that represents the energy of the particle ?This operator is called the Hamiltonian of the particle , and usually given the symbolˆH.Hamiltonian is a linear differential operator .222ˆ(,)2d V x t H m dx ⎡⎤-+ψ≡ψ⎢⎥⎣⎦h Kineticenergy Potential energyHence there is an alternative (shorthand) form for thetime-dependent Schrödinger equation:Part 3Time-independent Schrödinger equation (TISE), i.e.stationary state(定态)Schrödinger equationSuppose potential is independent of time(),()U x t U x =Look for a separated solution, substitute (,)()()x t x T t ψψ=into• This only tells us that T(t) depends on the energy E . It doesn’t tell us what the energy actually is. For that we have to solve the space part.• T(t) does not depend explicitly on the potential U(x). But there is an implicit dependencebecause the potential affectsthe possible values for the energy E .This is the time-independent Schrödinger equation (TISE) or so-called stationary state Schrödinger equation.Solution to full TDSE isEven though the potential is independent of time the wavefunction still oscillates in time . But probability distribution is static()()2*//2*,,()()()()()iEt iEt P x t x t x e x e x x x ψψψψψ+-=ψ===h hFor this reason a solution of the TISE is known as a StationaryState(定态)Stationary state Schrödinger Equation Notes:• In one-dimension space, the TISE is an ordinary differential equation (not a partial differential equation)• The TISE is an eigenvalue equation for the Hamiltonianoperator:ˆ()()Hx E x ψψ=Part 4 Probability current density and continuity equation Definition of probability current densityIn non-relativistic quantum mechanics, the probability current of the wave function Ψ is defined asin the position basis and satisfies the quantum mechanical continuity equationwith the probability density defined as.If one were to integrate both sides of the continuity equation with respect to volume, so thatthen the divergence theorem implies the continuity equation is equivalent to the integral equationwhere the V is any volume and S is the boundary of V. This is the conservation law for probability in quantum mechanics.In particular, if is a wavefunction describing a single particle, theintegral in the first term of the preceding equation (without the time derivative) is the probability of obtaining a value within V when the position of the particle is measured. The second term is then the rate at which probability is flowing out of the volume V. Altogether the equation states that the time derivative of the change of the probability of the particle being measured in V is equal to the rate at which probability flows into V. Derivation of continuity equationThe continuity equation is derived from the definition of probability current and the basic principles of quantum mechanics. Suppose is the wavefunction for a single particle in the positionbasis (i.e. is a function of x, y, and z). Thenis the probability that a measurement of the particle's position will yield a value within V. The time derivative of this iswhere the last equality follows from the product rule and the fact that the shape of V is presumed to be independent of time (i.e. the time derivative can be moved through the integral). In order to simplify this further, consider the time dependent Schrödinger equationand use it to solve for the time derivative of :When substituted back into the preceding equation for this gives.Now from the product rule for the divergence operatorand since the first and third terms cancel:If we now recall the expression for P and note that the argumentof the divergence operator is justthis becomeswhich is the integral form of the continuity equation .The differential form follows from the fact that the preceding equation holds for all V, and as the integrand is a continuousfunction of space, it must vanish everywhere:For all whole space we have()()2lim lim 0lim lim 0V V V V V S V S dV j dV t j dV j ds →∞→∞→→∞→∞⎛⎫∂ψ ⎪=-∇⋅= ⎪∂⎝⎭∇⋅=⋅=⎰⎰⎰⎰⎰⎰⎰⎰⎰⎰⎰r r r r rwhich meansthat must be continuousat any positionin the whole space.So the wavefunction and its derivative must be continuous.(An exception to this rule occurs when V is infinite.)One more, if the(,)()Et i x t x e ϕ-ψ=hand ()x ϕis real, the probability current*Im ()()0j x x m ϕϕ⎡⎤=∇≡⎣⎦r r h over the whole 1D space which means j r is always continuous whatever the wavefunction ()x ϕand its derivative ()x ϕ'are continuous or not. However, ()x ϕhas to be continuous for an acceptable physical solution for that the probability density is uniquely defined(唯一确定). As to ()x ϕ', it may not be continuous especially at the point where the potential energy is infinite.It is easy to prove that ()x ϕ' has to be continuous at the point 0x where the potential energy just has a limited high step.Have a fun!。

量子力学复习题

3.6 算符与力学量的关系（续５）
Chap.3 The Dynamical variable in Quantum Mechanism
F Cn n C d
2 2 n
EX１求在能量本征态 n ( x) 量和动能的平均值 Solve
L * n
2 n x sin( ) 下，动 L L
ˆx, p ˆy, p ˆ z 彼此对易，它们有共同的 Ex.1 动量算符 p
本征函数完备系 i pr 3 2 (r ) (2) p e ( r ) 描述的状态中， px , p y , pz 同时有确定值。在 p
ˆ ,L ˆ2 ] 0 ˆ2 和 L ˆ 对易，即 [ L Ex.2 角动量算符 L z z
( 2a 0 )
2
e

e
i pr cos
r 2 sin drdd

2
(2a0 )
2i
3
2
e
0 1 2
1
r a0
e

i pr cos
r drd cos
2 i pr

p (2a0 )
3
re
0

r a0
[e

i pr
e
]dr
Chap.3 The Dynamical variable in Quantum Mechanism
思考题（1）若两个厄米算符有共同本征态，它们是否就彼此对易。（2）若两个厄米算符不对易，是否一定就没有共同本征态。（3）若两个厄米算符对易，是否在所有态下它们都同时具有确定值。 ˆ, B ˆ ] =常数，A ˆ 能否有共同本征态。 ˆ 和B （4）若 [ A ˆ 和L ˆ （5）角动量分量 L 能否有共同本征态。 x y

路径积分分子动力学

路径积分分子动力学Path integral molecular dynamics (PIMD) is a computational method used to simulate the behavior of molecules in a system. It combines the principles of molecular dynamics with the path integral formulation of quantum mechanics, allowing for the investigation of quantum effects in molecular systems. PIMD is particularly useful in studying systems at low temperatures, where quantum effects become significant.One of the main advantages of PIMD is its ability to accurately describe the nuclear quantum effects that are present in molecular systems. In classical molecular dynamics simulations, the motion of atoms is described classically, neglecting their quantum nature. However, at low temperatures, the wave-like nature of atoms becomes important, and classical simulations fail to capture the correct behavior. PIMD overcomes this limitation by treating the atoms as quantum particles, allowing for the inclusion of nuclear quantum effects.PIMD works by transforming the quantum mechanical problem of a many-particle system into an equivalent classical problem in a higher-dimensional space. This is done by introducing a set of fictitious particles, known as replicas, that represent different paths of the system. These replicas are then propagated in time using classical molecular dynamics algorithms, incorporating both the quantum and classical aspects of the system. By averaging over the trajectories of the replicas, one can obtain thermodynamic properties and dynamical information of the system.The inclusion of nuclear quantum effects in PIMD simulations has important implications for understanding a variety of phenomena in molecular systems. For example, it can provide insights into the behavior of hydrogen bonds, which are crucial for the stability and function of biomolecules. PIMD can also be used to study the dynamics of chemical reactions, where quantum effects can significantly influence reaction rates and mechanisms. Furthermore, PIMD is valuable in investigating theproperties of materials at extreme conditions, such as high pressures and temperatures, where quantum effects become more pronounced.Despite its advantages, PIMD simulations can be computationally expensive due to the need to propagate multiple replicas. The computational cost increases withthe number of replicas, making it challenging to simulate large systems or perform long-time scale simulations. However, advancements in hardware and algorithms have made PIMD more accessible, allowing for the study ofincreasingly complex molecular systems.In conclusion, path integral molecular dynamics is a powerful computational method that combines classical molecular dynamics with the path integral formulation of quantum mechanics. It enables the investigation of nuclear quantum effects in molecular systems, providing valuable insights into the behavior of molecules at low temperatures. PIMD has diverse applications, ranging from the study of hydrogen bonds and chemical reactions to the exploration of materials under extreme conditions. While computationalcosts can be a limitation, ongoing developments in hardware and algorithms are expanding the scope of PIMD simulations.。

QuantumATK机器学习强迫场与物理学模型说明书

Machine-Learned Force Fields with QuantumATK/silicon/quantumatk/atomistic-simulation-products/machine-learned-force-fields.htmlTemplates & GUI • Use automatic training tools and GUI templates [1,2] for : - crystal & amorphous bulk materials - interfaces - molecules • Inspect automatically generated training configurations using GUI • Validate generated ML FFs by comparing calculated values with available experimental and DFT data: - RDF and ADF - Elastic constants - Neutron scattering factor - Chemical composition profile- X-ray scattering QuantumATK Advantages• Automated user-friendly generation of training data, tailored for specific applications - Ensures minimal amount of training data and time needed - No computationally expensive ab-initio MD is needed in most cases - Provides good quality accurate ML FFs for complex systems • Single interface for different simulation engines - Easily switch between training with DFT-LCAO and DFT-PW - Combine ML FFs with conventional FFs, DFT or Semi-empirical calculatorsAutomatic Workflows Basic workflow • For crystalline materials • Automatically generate training configurations, compute training data with DFT, and perform machine learning, i.e., fitting to the training data Advanced active learning workflow • For amorphous systems, interfaces, systems at high T, surface processes • Improve initial ML FFs generated with the basic workflow by actively adding training configurations and DFT training data during MDsimulations Machine-Learned Force Fields (ML FFs) provide near -ab initio accuracy for large realistic system sizes and dynamical simulation time-scales greatly exceeding those accessible to Density Functional Theory (DFT). Use ML FFs in QuantumATK to generate realistic complex structures of novel crystal and amorphous materials, alloys, interfaces, and multilayer stacks, simulate thermal and mechanical properties, diffusion and surface processes. Benefit from the pre-trained ML FF library or develop new ML FFs using automated and efficient training and simulation workflows. Employ ML FFs for molecular dynamics (MD), force bias Monte Carlo, nudged elastic band (NEB), and geometry optimization simulations.• 1000 to 10,000x faster than DFT , thus enabling dynam-ical modeling of realistic novel and complex systems containing even 100,000+ atoms, instead of small model 100-atom systems.• Provide near-ab initio accuracy for multi-element materi-als, heterogeneous systems like interfaces, and systems far from equilibrium, including amorphous materials, phase transitions, or chemical reactions.• Often easier to develop than conventional FFs using the automated workflows available in QuantumATK. Accu -rate conventional FFs for such complex materials would require much more extensive and complicated develop-ment processes.ML FFs for Dynamical Simulations of Large-Scale Realistic SystemsAutomated Efficient Generation of ML FFs2Synopsys QuantumATK Team Fruebjergvej 3DK-2100 Copenhagen DENMARK /quantumatk ***********************+45 333 32 300©2022 Synopsys, Inc. All rights reserved. Synopsys is a trademark of Synopsys, Inc. in the United States and other countries. A list of Synopsys trademarks is available at https:///copyright.html . All other names mentioned herein are trademarks of their respective owners.Application Examples of Machine-Learned Force FieldsStructure Generation of Amorphous Materials: Generate amorphous structures for PCRAM, ReRAM and FeRAM novel memories, solar cell and other applications. In this example, 80 ps ML FF - MD generated am-SiO 2 structure of 600 atoms in 11 minutes, whereas it took 10 days to generate 72-atom structure with DFT-MD on 16 cores. Structural parameters obtained with ML FFs are in a good agreement with DFT and experimental results.development applications, such as high-k metal gate (HKMG) (using Multilayer builder GUI ) and MRAM magnetic tunnel junction engineering. This example shows a generated structure of Structure Generation of Glassy Amorphous Materials: Generate glassy amorphous materials with impurities for optoelectronic applications. In this example, ML FF – MD is used to simulate a large- scale 120,000 atom size sodium silicate glass with Na impurities, (Na 2O)2(SiO 2)40000 at 2500 K.Thermal Property Simulations : Simulate thermal conductance using ML FFs with ns -long reverse non-equilibrium MD (RNEMD) simulations for developing PCRAM and evaluating self-heating and heat dissipation in devices. Examples include simulating thermal conductance in bulk Ge 2Sb 2Te 5 (2300 atoms), Ge 2Sb 2Te 5/Si (882 atoms) and Si/GaAs (864 atoms) interfaces, monolayer MoS 2(108,000 atoms). Calculated values are in a good agreement with experimentaland DFT results where available.Built-in Library of Ready-to-Use Machine-Learned Force Fields►QuantumATK offers Moment Tensor Potentials (MTPs) ML FFs implemented by the QuantumATK team in-house. ►MTPs provide high robust accuracy with lower computational cost compared to other ML FFs [3,4]. ►Benefit from the pre-trained ready-to-use high-quality MTP library [5,6] or develop MTPs for new materials, interfaces and surface processes by using automatic generation workflows.Tutorial and video on automatic ML FF training tools and GUI templates[1] Tutorial: https:///tutorials/mtp_hfo2/mtp_hfo2.html [2] Video: https:///watch?v=6BrrVotzjnc[3] A. V. Shapeev. Moment tensor potentials: a class of systematically improvable interatomic potentials. Multiscale Model. & Simul. 14, 1153 (2016).[4] Y. Zuo, C. Chen, X. Li, Z. Deng, Y. Chen, J. Behler, G. Csányi, A. V. Shapeev, A. P . Thompson, M. A. Wood, and S. Ping Ong. Performance and cost assessment of machine learning interatomic potentials . J. Phys. Chem. A 124, 731(2020).[5] ML FF features: https:///silicon/quantumatk/resources/feature-list.html#MLforcefield[6] Materials in ML FF library: https:///manual/ForceField.html#pretrained-moment-tensor-potential-mtp-parameter-sets。

量子力学教程Ch32

经典力学中物质运动的状态总用坐标、动量、角动量、自旋、动能、势能、转动能等力学量以决定论的方式描述。而量子力学的第一个惊人之举就是引入
了波函数这样一个基本概念，以概率的特征全面地
描述了微观粒子的运动状态。但并不能作为量子力
学中的力学量。于是，又引入了一个重要的基本概念——算符，用它表示量子力学中的力学量。算符与波函数作为量子力学的核心概念相辅相成、贯穿始终。
若已知粒子在坐标表象中的状态波函数 (r,t) ，
按子照坐波标函(x统, y计, z)解或释rr，的利平用均统值计平均方法，可求得粒
若知道粒子在动量表象中的波函数 C( p,t) ，同理
可求出粒子动量
(Px , Py , Pz )或
P
的平均值。
6
3.1 表示力学量的算符（续1）
Chap.3 The Dynamical variable in Quantum Mechanism
r
C
*
(
P,
t
)rˆC
(
P, t
)d
3
P
rvˆ
ihP
r ih i
Px
r j
Py
v k
Pz
称为坐标算符
Prove： r *(r,t)r (r,t)d3r
1
*(rv,t)rv[
C
(
v P,
t
)e
i h
Pvrv
d
3
v P]d
3rv
(2 h)3/2
1 *(rv,t)[
(2 h)3/2
Chap.3 The Dynamical variable in Quantum Mechanism
第三章量子力学中的力学量

物理学专业英语

华中师范大学物理学院物理学专业英语仅供内部学习参考！2014一、课程的任务和教学目的通过学习《物理学专业英语》，学生将掌握物理学领域使用频率较高的专业词汇和表达方法，进而具备基本的阅读理解物理学专业文献的能力。

通过分析《物理学专业英语》课程教材中的范文，学生还将从英语角度理解物理学中个学科的研究内容和主要思想，提高学生的专业英语能力和了解物理学研究前沿的能力。

培养专业英语阅读能力，了解科技英语的特点，提高专业外语的阅读质量和阅读速度；掌握一定量的本专业英文词汇，基本达到能够独立完成一般性本专业外文资料的阅读；达到一定的笔译水平。

要求译文通顺、准确和专业化。

二、课程内容课程内容包括以下章节：物理学、经典力学、热力学、电磁学、光学、原子物理、统计力学、量子力学和狭义相对论三、基本要求1.充分利用课内时间保证充足的阅读量（约1200~1500词/学时），要求正确理解原文。

2.泛读适量课外相关英文读物，要求基本理解原文主要内容。

3.掌握基本专业词汇（不少于200词）。

4.应具有流利阅读、翻译及赏析专业英语文献，并能简单地进行写作的能力。

四、参考书目录1 Physics 物理学 (1)Introduction to physics (1)Classical and modern physics (2)Research fields (4)V ocabulary (7)2 Classical mechanics 经典力学 (10)Introduction (10)Description of classical mechanics (10)Momentum and collisions (14)Angular momentum (15)V ocabulary (16)3 Thermodynamics 热力学 (18)Introduction (18)Laws of thermodynamics (21)System models (22)Thermodynamic processes (27)Scope of thermodynamics (29)V ocabulary (30)4 Electromagnetism 电磁学 (33)Introduction (33)Electrostatics (33)Magnetostatics (35)Electromagnetic induction (40)V ocabulary (43)5 Optics 光学 (45)Introduction (45)Geometrical optics (45)Physical optics (47)Polarization (50)V ocabulary (51)6 Atomic physics 原子物理 (52)Introduction (52)Electronic configuration (52)Excitation and ionization (56)V ocabulary (59)7 Statistical mechanics 统计力学 (60)Overview (60)Fundamentals (60)Statistical ensembles (63)V ocabulary (65)8 Quantum mechanics 量子力学 (67)Introduction (67)Mathematical formulations (68)Quantization (71)Wave-particle duality (72)Quantum entanglement (75)V ocabulary (77)9 Special relativity 狭义相对论 (79)Introduction (79)Relativity of simultaneity (80)Lorentz transformations (80)Time dilation and length contraction (81)Mass-energy equivalence (82)Relativistic energy-momentum relation (86)V ocabulary (89)正文标记说明：蓝色Arial字体（例如energy）：已知的专业词汇蓝色Arial字体加下划线（例如electromagnetism）：新学的专业词汇黑色Times New Roman字体加下划线（例如postulate）：新学的普通词汇1 Physics 物理学1 Physics 物理学Introduction to physicsPhysics is a part of natural philosophy and a natural science that involves the study of matter and its motion through space and time, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic disciplines, perhaps the oldest through its inclusion of astronomy. Over the last two millennia, physics was a part of natural philosophy along with chemistry, certain branches of mathematics, and biology, but during the Scientific Revolution in the 17th century, the natural sciences emerged as unique research programs in their own right. Physics intersects with many interdisciplinary areas of research, such as biophysics and quantum chemistry,and the boundaries of physics are not rigidly defined. New ideas in physics often explain the fundamental mechanisms of other sciences, while opening new avenues of research in areas such as mathematics and philosophy.Physics also makes significant contributions through advances in new technologies that arise from theoretical breakthroughs. For example, advances in the understanding of electromagnetism or nuclear physics led directly to the development of new products which have dramatically transformed modern-day society, such as television, computers, domestic appliances, and nuclear weapons; advances in thermodynamics led to the development of industrialization; and advances in mechanics inspired the development of calculus.Core theoriesThough physics deals with a wide variety of systems, certain theories are used by all physicists. Each of these theories were experimentally tested numerous times and found correct as an approximation of nature (within a certain domain of validity).For instance, the theory of classical mechanics accurately describes the motion of objects, provided they are much larger than atoms and moving at much less than the speed of light. These theories continue to be areas of active research, and a remarkable aspect of classical mechanics known as chaos was discovered in the 20th century, three centuries after the original formulation of classical mechanics by Isaac Newton (1642–1727) 【艾萨克·牛顿】.University PhysicsThese central theories are important tools for research into more specialized topics, and any physicist, regardless of his or her specialization, is expected to be literate in them. These include classical mechanics, quantum mechanics, thermodynamics and statistical mechanics, electromagnetism, and special relativity.Classical and modern physicsClassical mechanicsClassical physics includes the traditional branches and topics that were recognized and well-developed before the beginning of the 20th century—classical mechanics, acoustics, optics, thermodynamics, and electromagnetism.Classical mechanics is concerned with bodies acted on by forces and bodies in motion and may be divided into statics (study of the forces on a body or bodies at rest), kinematics (study of motion without regard to its causes), and dynamics (study of motion and the forces that affect it); mechanics may also be divided into solid mechanics and fluid mechanics (known together as continuum mechanics), the latter including such branches as hydrostatics, hydrodynamics, aerodynamics, and pneumatics.Acoustics is the study of how sound is produced, controlled, transmitted and received. Important modern branches of acoustics include ultrasonics, the study of sound waves of very high frequency beyond the range of human hearing; bioacoustics the physics of animal calls and hearing, and electroacoustics, the manipulation of audible sound waves using electronics.Optics, the study of light, is concerned not only with visible light but also with infrared and ultraviolet radiation, which exhibit all of the phenomena of visible light except visibility, e.g., reflection, refraction, interference, diffraction, dispersion, and polarization of light.Heat is a form of energy, the internal energy possessed by the particles of which a substance is composed; thermodynamics deals with the relationships between heat and other forms of energy.Electricity and magnetism have been studied as a single branch of physics since the intimate connection between them was discovered in the early 19th century; an electric current gives rise to a magnetic field and a changing magnetic field induces an electric current. Electrostatics deals with electric charges at rest, electrodynamics with moving charges, and magnetostatics with magnetic poles at rest.Modern PhysicsClassical physics is generally concerned with matter and energy on the normal scale of1 Physics 物理学observation, while much of modern physics is concerned with the behavior of matter and energy under extreme conditions or on the very large or very small scale.For example, atomic and nuclear physics studies matter on the smallest scale at which chemical elements can be identified.The physics of elementary particles is on an even smaller scale, as it is concerned with the most basic units of matter; this branch of physics is also known as high-energy physics because of the extremely high energies necessary to produce many types of particles in large particle accelerators. On this scale, ordinary, commonsense notions of space, time, matter, and energy are no longer valid.The two chief theories of modern physics present a different picture of the concepts of space, time, and matter from that presented by classical physics.Quantum theory is concerned with the discrete, rather than continuous, nature of many phenomena at the atomic and subatomic level, and with the complementary aspects of particles and waves in the description of such phenomena.The theory of relativity is concerned with the description of phenomena that take place in a frame of reference that is in motion with respect to an observer; the special theory of relativity is concerned with relative uniform motion in a straight line and the general theory of relativity with accelerated motion and its connection with gravitation.Both quantum theory and the theory of relativity find applications in all areas of modern physics.Difference between classical and modern physicsWhile physics aims to discover universal laws, its theories lie in explicit domains of applicability. Loosely speaking, the laws of classical physics accurately describe systems whose important length scales are greater than the atomic scale and whose motions are much slower than the speed of light. Outside of this domain, observations do not match their predictions.Albert Einstein【阿尔伯特·爱因斯坦】contributed the framework of special relativity, which replaced notions of absolute time and space with space-time and allowed an accurate description of systems whose components have speeds approaching the speed of light.Max Planck【普朗克】, Erwin Schrödinger【薛定谔】, and others introduced quantum mechanics, a probabilistic notion of particles and interactions that allowed an accurate description of atomic and subatomic scales.Later, quantum field theory unified quantum mechanics and special relativity.General relativity allowed for a dynamical, curved space-time, with which highly massiveUniversity Physicssystems and the large-scale structure of the universe can be well-described. General relativity has not yet been unified with the other fundamental descriptions; several candidate theories of quantum gravity are being developed.Research fieldsContemporary research in physics can be broadly divided into condensed matter physics; atomic, molecular, and optical physics; particle physics; astrophysics; geophysics and biophysics. Some physics departments also support research in Physics education.Since the 20th century, the individual fields of physics have become increasingly specialized, and today most physicists work in a single field for their entire careers. "Universalists" such as Albert Einstein (1879–1955) and Lev Landau (1908–1968)【列夫·朗道】, who worked in multiple fields of physics, are now very rare.Condensed matter physicsCondensed matter physics is the field of physics that deals with the macroscopic physical properties of matter. In particular, it is concerned with the "condensed" phases that appear whenever the number of particles in a system is extremely large and the interactions between them are strong.The most familiar examples of condensed phases are solids and liquids, which arise from the bonding by way of the electromagnetic force between atoms. More exotic condensed phases include the super-fluid and the Bose–Einstein condensate found in certain atomic systems at very low temperature, the superconducting phase exhibited by conduction electrons in certain materials,and the ferromagnetic and antiferromagnetic phases of spins on atomic lattices.Condensed matter physics is by far the largest field of contemporary physics.Historically, condensed matter physics grew out of solid-state physics, which is now considered one of its main subfields. The term condensed matter physics was apparently coined by Philip Anderson when he renamed his research group—previously solid-state theory—in 1967. In 1978, the Division of Solid State Physics of the American Physical Society was renamed as the Division of Condensed Matter Physics.Condensed matter physics has a large overlap with chemistry, materials science, nanotechnology and engineering.Atomic, molecular and optical physicsAtomic, molecular, and optical physics (AMO) is the study of matter–matter and light–matter interactions on the scale of single atoms and molecules.1 Physics 物理学The three areas are grouped together because of their interrelationships, the similarity of methods used, and the commonality of the energy scales that are relevant. All three areas include both classical, semi-classical and quantum treatments; they can treat their subject from a microscopic view (in contrast to a macroscopic view).Atomic physics studies the electron shells of atoms. Current research focuses on activities in quantum control, cooling and trapping of atoms and ions, low-temperature collision dynamics and the effects of electron correlation on structure and dynamics. Atomic physics is influenced by the nucleus (see, e.g., hyperfine splitting), but intra-nuclear phenomena such as fission and fusion are considered part of high-energy physics.Molecular physics focuses on multi-atomic structures and their internal and external interactions with matter and light.Optical physics is distinct from optics in that it tends to focus not on the control of classical light fields by macroscopic objects, but on the fundamental properties of optical fields and their interactions with matter in the microscopic realm.High-energy physics (particle physics) and nuclear physicsParticle physics is the study of the elementary constituents of matter and energy, and the interactions between them.In addition, particle physicists design and develop the high energy accelerators,detectors, and computer programs necessary for this research. The field is also called "high-energy physics" because many elementary particles do not occur naturally, but are created only during high-energy collisions of other particles.Currently, the interactions of elementary particles and fields are described by the Standard Model.●The model accounts for the 12 known particles of matter (quarks and leptons) thatinteract via the strong, weak, and electromagnetic fundamental forces.●Dynamics are described in terms of matter particles exchanging gauge bosons (gluons,W and Z bosons, and photons, respectively).●The Standard Model also predicts a particle known as the Higgs boson. In July 2012CERN, the European laboratory for particle physics, announced the detection of a particle consistent with the Higgs boson.Nuclear Physics is the field of physics that studies the constituents and interactions of atomic nuclei. The most commonly known applications of nuclear physics are nuclear power generation and nuclear weapons technology, but the research has provided application in many fields, including those in nuclear medicine and magnetic resonance imaging, ion implantation in materials engineering, and radiocarbon dating in geology and archaeology.University PhysicsAstrophysics and Physical CosmologyAstrophysics and astronomy are the application of the theories and methods of physics to the study of stellar structure, stellar evolution, the origin of the solar system, and related problems of cosmology. Because astrophysics is a broad subject, astrophysicists typically apply many disciplines of physics, including mechanics, electromagnetism, statistical mechanics, thermodynamics, quantum mechanics, relativity, nuclear and particle physics, and atomic and molecular physics.The discovery by Karl Jansky in 1931 that radio signals were emitted by celestial bodies initiated the science of radio astronomy. Most recently, the frontiers of astronomy have been expanded by space exploration. Perturbations and interference from the earth's atmosphere make space-based observations necessary for infrared, ultraviolet, gamma-ray, and X-ray astronomy.Physical cosmology is the study of the formation and evolution of the universe on its largest scales. Albert Einstein's theory of relativity plays a central role in all modern cosmological theories. In the early 20th century, Hubble's discovery that the universe was expanding, as shown by the Hubble diagram, prompted rival explanations known as the steady state universe and the Big Bang.The Big Bang was confirmed by the success of Big Bang nucleo-synthesis and the discovery of the cosmic microwave background in 1964. The Big Bang model rests on two theoretical pillars: Albert Einstein's general relativity and the cosmological principle (On a sufficiently large scale, the properties of the Universe are the same for all observers). Cosmologists have recently established the ΛCDM model (the standard model of Big Bang cosmology) of the evolution of the universe, which includes cosmic inflation, dark energy and dark matter.Current research frontiersIn condensed matter physics, an important unsolved theoretical problem is that of high-temperature superconductivity. Many condensed matter experiments are aiming to fabricate workable spintronics and quantum computers.In particle physics, the first pieces of experimental evidence for physics beyond the Standard Model have begun to appear. Foremost among these are indications that neutrinos have non-zero mass. These experimental results appear to have solved the long-standing solar neutrino problem, and the physics of massive neutrinos remains an area of active theoretical and experimental research. Particle accelerators have begun probing energy scales in the TeV range, in which experimentalists are hoping to find evidence for the super-symmetric particles, after discovery of the Higgs boson.Theoretical attempts to unify quantum mechanics and general relativity into a single theory1 Physics 物理学of quantum gravity, a program ongoing for over half a century, have not yet been decisively resolved. The current leading candidates are M-theory, superstring theory and loop quantum gravity.Many astronomical and cosmological phenomena have yet to be satisfactorily explained, including the existence of ultra-high energy cosmic rays, the baryon asymmetry, the acceleration of the universe and the anomalous rotation rates of galaxies.Although much progress has been made in high-energy, quantum, and astronomical physics, many everyday phenomena involving complexity, chaos, or turbulence are still poorly understood. Complex problems that seem like they could be solved by a clever application of dynamics and mechanics remain unsolved; examples include the formation of sand-piles, nodes in trickling water, the shape of water droplets, mechanisms of surface tension catastrophes, and self-sorting in shaken heterogeneous collections.These complex phenomena have received growing attention since the 1970s for several reasons, including the availability of modern mathematical methods and computers, which enabled complex systems to be modeled in new ways. Complex physics has become part of increasingly interdisciplinary research, as exemplified by the study of turbulence in aerodynamics and the observation of pattern formation in biological systems.Vocabulary★natural science 自然科学academic disciplines 学科astronomy 天文学in their own right 凭他们本身的实力intersects相交，交叉interdisciplinary交叉学科的，跨学科的★quantum 量子的theoretical breakthroughs 理论突破★electromagnetism 电磁学dramatically显著地★thermodynamics热力学★calculus微积分validity★classical mechanics 经典力学chaos 混沌literate 学者★quantum mechanics量子力学★thermodynamics and statistical mechanics热力学与统计物理★special relativity狭义相对论is concerned with 关注，讨论，考虑acoustics 声学★optics 光学statics静力学at rest 静息kinematics运动学★dynamics动力学ultrasonics超声学manipulation 操作，处理，使用University Physicsinfrared红外ultraviolet紫外radiation辐射reflection 反射refraction 折射★interference 干涉★diffraction 衍射dispersion散射★polarization 极化，偏振internal energy 内能Electricity电性Magnetism 磁性intimate 亲密的induces 诱导，感应scale尺度★elementary particles基本粒子★high-energy physics 高能物理particle accelerators 粒子加速器valid 有效的，正当的★discrete离散的continuous 连续的complementary 互补的★frame of reference 参照系★the special theory of relativity 狭义相对论★general theory of relativity 广义相对论gravitation 重力，万有引力explicit 详细的，清楚的★quantum field theory 量子场论★condensed matter physics凝聚态物理astrophysics天体物理geophysics地球物理Universalist博学多才者★Macroscopic宏观Exotic奇异的★Superconducting 超导Ferromagnetic铁磁质Antiferromagnetic 反铁磁质★Spin自旋Lattice 晶格，点阵，网格★Society社会，学会★microscopic微观的hyperfine splitting超精细分裂fission分裂，裂变fusion熔合，聚变constituents成分，组分accelerators加速器detectors 检测器★quarks夸克lepton 轻子gauge bosons规范玻色子gluons胶子★Higgs boson希格斯玻色子CERN欧洲核子研究中心★Magnetic Resonance Imaging磁共振成像，核磁共振ion implantation 离子注入radiocarbon dating放射性碳年代测定法geology地质学archaeology考古学stellar 恒星cosmology宇宙论celestial bodies 天体Hubble diagram 哈勃图Rival竞争的★Big Bang大爆炸nucleo-synthesis核聚合，核合成pillar支柱cosmological principle宇宙学原理ΛCDM modelΛ-冷暗物质模型cosmic inflation宇宙膨胀1 Physics 物理学fabricate制造，建造spintronics自旋电子元件，自旋电子学★neutrinos 中微子superstring 超弦baryon重子turbulence湍流，扰动，骚动catastrophes突变，灾变，灾难heterogeneous collections异质性集合pattern formation模式形成University Physics2 Classical mechanics 经典力学IntroductionIn physics, classical mechanics is one of the two major sub-fields of mechanics, which is concerned with the set of physical laws describing the motion of bodies under the action of a system of forces. The study of the motion of bodies is an ancient one, making classical mechanics one of the oldest and largest subjects in science, engineering and technology.Classical mechanics describes the motion of macroscopic objects, from projectiles to parts of machinery, as well as astronomical objects, such as spacecraft, planets, stars, and galaxies. Besides this, many specializations within the subject deal with gases, liquids, solids, and other specific sub-topics.Classical mechanics provides extremely accurate results as long as the domain of study is restricted to large objects and the speeds involved do not approach the speed of light. When the objects being dealt with become sufficiently small, it becomes necessary to introduce the other major sub-field of mechanics, quantum mechanics, which reconciles the macroscopic laws of physics with the atomic nature of matter and handles the wave–particle duality of atoms and molecules. In the case of high velocity objects approaching the speed of light, classical mechanics is enhanced by special relativity. General relativity unifies special relativity with Newton's law of universal gravitation, allowing physicists to handle gravitation at a deeper level.The initial stage in the development of classical mechanics is often referred to as Newtonian mechanics, and is associated with the physical concepts employed by and the mathematical methods invented by Newton himself, in parallel with Leibniz【莱布尼兹】, and others.Later, more abstract and general methods were developed, leading to reformulations of classical mechanics known as Lagrangian mechanics and Hamiltonian mechanics. These advances were largely made in the 18th and 19th centuries, and they extend substantially beyond Newton's work, particularly through their use of analytical mechanics. Ultimately, the mathematics developed for these were central to the creation of quantum mechanics.Description of classical mechanicsThe following introduces the basic concepts of classical mechanics. For simplicity, it often2 Classical mechanics 经典力学models real-world objects as point particles, objects with negligible size. The motion of a point particle is characterized by a small number of parameters: its position, mass, and the forces applied to it.In reality, the kind of objects that classical mechanics can describe always have a non-zero size. (The physics of very small particles, such as the electron, is more accurately described by quantum mechanics). Objects with non-zero size have more complicated behavior than hypothetical point particles, because of the additional degrees of freedom—for example, a baseball can spin while it is moving. However, the results for point particles can be used to study such objects by treating them as composite objects, made up of a large number of interacting point particles. The center of mass of a composite object behaves like a point particle.Classical mechanics uses common-sense notions of how matter and forces exist and interact. It assumes that matter and energy have definite, knowable attributes such as where an object is in space and its speed. It also assumes that objects may be directly influenced only by their immediate surroundings, known as the principle of locality.In quantum mechanics objects may have unknowable position or velocity, or instantaneously interact with other objects at a distance.Position and its derivativesThe position of a point particle is defined with respect to an arbitrary fixed reference point, O, in space, usually accompanied by a coordinate system, with the reference point located at the origin of the coordinate system. It is defined as the vector r from O to the particle.In general, the point particle need not be stationary relative to O, so r is a function of t, the time elapsed since an arbitrary initial time.In pre-Einstein relativity (known as Galilean relativity), time is considered an absolute, i.e., the time interval between any given pair of events is the same for all observers. In addition to relying on absolute time, classical mechanics assumes Euclidean geometry for the structure of space.Velocity and speedThe velocity, or the rate of change of position with time, is defined as the derivative of the position with respect to time. In classical mechanics, velocities are directly additive and subtractive as vector quantities; they must be dealt with using vector analysis.When both objects are moving in the same direction, the difference can be given in terms of speed only by ignoring direction.University PhysicsAccelerationThe acceleration , or rate of change of velocity, is the derivative of the velocity with respect to time (the second derivative of the position with respect to time).Acceleration can arise from a change with time of the magnitude of the velocity or of the direction of the velocity or both . If only the magnitude v of the velocity decreases, this is sometimes referred to as deceleration , but generally any change in the velocity with time, including deceleration, is simply referred to as acceleration.Inertial frames of referenceWhile the position and velocity and acceleration of a particle can be referred to any observer in any state of motion, classical mechanics assumes the existence of a special family of reference frames in terms of which the mechanical laws of nature take a comparatively simple form. These special reference frames are called inertial frames .An inertial frame is such that when an object without any force interactions (an idealized situation) is viewed from it, it appears either to be at rest or in a state of uniform motion in a straight line. This is the fundamental definition of an inertial frame. They are characterized by the requirement that all forces entering the observer's physical laws originate in identifiable sources (charges, gravitational bodies, and so forth).A non-inertial reference frame is one accelerating with respect to an inertial one, and in such a non-inertial frame a particle is subject to acceleration by fictitious forces that enter the equations of motion solely as a result of its accelerated motion, and do not originate in identifiable sources. These fictitious forces are in addition to the real forces recognized in an inertial frame.A key concept of inertial frames is the method for identifying them. For practical purposes, reference frames that are un-accelerated with respect to the distant stars are regarded as good approximations to inertial frames.Forces; Newton's second lawNewton was the first to mathematically express the relationship between force and momentum . Some physicists interpret Newton's second law of motion as a definition of force and mass, while others consider it a fundamental postulate, a law of nature. Either interpretation has the same mathematical consequences, historically known as "Newton's Second Law":a m t v m t p F ===d )(d d dThe quantity m v is called the (canonical ) momentum . The net force on a particle is thus equal to rate of change of momentum of the particle with time.So long as the force acting on a particle is known, Newton's second law is sufficient to。

PACC_国际物理学分类表_

如何查PACC代码？PACC代码是《Physics Abstracts,Classification and Contents》的缩略。

PACC专业代码是英国科学文摘（INSPEC）用于论文分类的代码。

按照论文的内容将其分为十大类有0000，1000，……5000，……9000表示，例如：凝聚物质由6000及7000表示，其中6000内包括凝聚物质的结构、热学和力学性质，而7000内包括凝聚物质的电子结构、电学、磁学和光学性质。

再仔细分则由6100……6200等表示，例如6100表示液体和固体结构。

而X射线晶体结构测定及精确化技术表示固体结构的测定包含在6100中，而用6110M来表示。

所以要查出某一论文的PACC专业代码，应先确定该论文主要内容属于哪一大类，就在那一大类中找出其代码，其次再找出该论文包括的其它次要内容的代码。

国际物理学分类表PACC（Physics Abstracts, Classification andContents）0000 总论 GENERAL0100 通讯、教育、历史和哲学 communication,education,history,andphilosophy0110 通报、消息和组织活动announcements, news, and organizational activities0110C 通报、消息和颁奖announcements, news, and awards 0110F 会议、演讲和学会conferences, lectures, and institutes 0110H 物理学组织活动physics organizational activities 0130 物理学文献及出版物physics literature and publications0130B 讲稿的出版(进修学院,暑期学校等)publications of lectures (advanced institutes, summer schools, etc.)0130C 会议录 conferenceproceedings 0130E 专著和著作集 monographs,andcollections 0130K 手册和字典handbooks and dictionaries0130L 物理数据、表格汇编collections of physical data, tables0130N 教科书 textbooks0130Q 报告、学位论文、论文reports, dissertations, theses0130R 评论及教学参考论文,资源通讯reviews and tutorial papers, resource letters0130T 书目 bibliographies 0140 教育 education0140D 课程设置与评价course design and evaluation0140E 中小学科学science in elementary and secondary school0140G 课程设置,教学方法,策略和评价curricula, teaching methods, strategies, and evaluation0140J 教师培训 teachertraining0150 教具(包括设备和实验及教学用材料)educational aids(inc.equipment, experiments andteaching approaches to subjects)0150F 视听教具、电影audio and visual aids, films0150H 计算机在教学中的使用instructional computer use0150K 试验理论和技术testing theory and techniques0150M 示范教学的实验和设备demonstration experiments and apparatus 0150P 实验室实验和设备laboratory experiments and apparatus0150Q 实验室课程设置、组织和评价laboratory course design, organization, and evaluation0150T 建筑物和设备 buildingsandfacilities 0155 普通物理 generalphysics 0160 传记、历史和个人笔记biographical, historical, and personal notes 0165 科学史history of science0170 科学哲学 philosophyofscience 0175 科学与社会 scienceandsociety 0190 其他一般论题other topics of general interest0200 物理学中的数学方法mathematical methods in physics0210 代数、集合论和图论algebra, set theory, and graph theory0220 群论(量子力学中的代数方法见0365;基本粒子物理学中的对称见1130)group theory(for algebraic methods in quantummechanics, see 0365; for symmetries inelementary particle physics, see 1130)0230 函数论,分析function theory, analysis0240 几何学、微分几何学和拓扑学(0400相对论与引力)geometry, differential geometry, andtopology(0400 relativity and gravitation)0250 概率论、随机过程和统计学(0500统计物理学)probability theory, stochastic processes, andstatistics(0500 statistical physics)0260 数字近似及分析numerical approximation and analysis0270 计算技术(数据处理与计算见0650)computational techniques(for data handling and computation, see 0650)0290 物理学中数学方法的其它论题other topics in mathematical methods in physics0300 经典及量子物理学;力学与场classical and quantum physics; mechanics and fields0320 离散系统的经典力学:一般数学问题(离散系统的应用经典力学见4610;天体力学见9510)classical mechanics of discrete systems: generalmathematical aspects ( for applied classicalmechanics of discrete systems, see 4610; forcelestial mechanics, see 9510)0330 狭义相对论 specialrelativity0340 连续介质经典力学:一般数学问题classical mechanics of continuous media: general mathematical aspects0340D 弹性力学的数学理论(4620连续介质力学,4630固体力学)mathematical theory of elasticity(4620 continuummechanics, and 4630 mechanics of solids)0340G 流体动力学:一般数学问题(4700流体动力学)fluid dynamics; general mathematicalaspects(4700 fluid dynamics)0340K 波和波传播:一般数学问题(4630M机械波和弹性波;4320一般线性声学)waves and wave propagation; generalmathematical aspects(4630M mechanical andelastic waves, 4320 general linear acoustics)0350 经典场论 classicalfieldtheory0350D 麦克斯韦理论:一般数学问题(应用经典电动力学,见4100)Maxwell theory: general mathematical aspects(forapplied classical electrodynamics, see 4100)0350K 其它具体经典场论other special classical field theories0365 量子论;量子力学(0530量子统计力学;相对论性波动方程,见1110)quantum theory; quantum mechanics(0530quantum statistical mechanics;for relativisticwave equations, see 1110)0365B 基础、测量理论、其它理论foundations, theory of measurement, miscellaneous theories0365C 形式论 formalism 0365D 泛函分析方法functional analytical methods0365F 代数方法(0220群论;3115分子物理学中计算方法)algebraic methods(02 20 group theory; 3115calculation methods in molecular physics)0365G 波动方程解:边界态solutions of wave equations: bound state0365N 非相对论性散射理论 nonrelativisticscatteringtheory 0365S 半经典理论和应用semiclassical theories and applications0367 量子信息 Quantuminformation 0370 量子场论(1110场论) theory of quantized fields(1110 field theory)0380 散射的一般理论(1120 S-矩阵论;1180相对论性散射)general theory of scattering(1120 S-matrix theory,and 1180 relativistic scattering)0400 相对论与引力(狭义相对论,见0330;相对论性天体物理学,见9530; 相对论性宇宙学,见9880)relativity and gravitation(for special relarivity,see0330;for relativistic astrophysics,see 9530;forrelativistic cosmology,see 9880)0420 广义相对论(0240几何学和拓扑学)general relativity (0240 geometry and topology) 0420C 基本问题和普通形式论fundamental problems and general formalism0420F 典型的形式论、拉氏函数和变分原理canonical formalism, Lagrangians, and variationalprinciples0420J 方程解solutions to equations0420M 守恒定律和运动方程conservation laws and equations of motion 0430 引力波和辐射:理论gravitational waves and radiation: theory0440 连续介质;电磁及其它混合引力系统continuous media; electromagnetic and othermixed gravitational systems0450 统一场论及其它引力理论unified field theories and other theories of gravitation0455 引力替代理论alternative theories of gravitation0460 引力的量子论quantum theory of gravitation0465 超引力 supergravity0470 黑洞物理学(参见9760L 黑洞) physics of black holes (see also 9760L black holes)0480 广义相对论的实验检验及引力辐射观测experimental tests of general relativity andobservations of gravitational radiation0485 中程力(包括第五和第六力) intermediate range forces (inc.fifth and sixth forces)0490 相对论和引力的其它论题other topics in relativity and gravitation0500 统计物理学和热力学(0250概率论、随机过程和统计学)statistical physics and thermodynamics(0250probability thory,stochastic processes,andstatistics)0520 统计力学 statisticalmechanics 0520D 分子运动论 kinetictheory0520G 经典系综论classical ensemble theory0530 量子统计力学(6700量子流体;7100凝聚物质的电子态)quantum statistic al mechanics(6700 quantumfluids, and 7100 electron states in condensedmatter)0530C 量子系综论quantum ensemble theory0530F 费米子系统和电子气Fermion systems and electron gas 0530J 玻色子系统 Bosonsystems0530L 任意子和仲统计学(量子统计力学)anyons and parastatistics (quantum statistical mechanics)0540 涨落现象、随机过程和布朗运动fluctuation phenomena, random processes, and Brownian motion0545 混沌系统的理论和模型(流体系统中的混沌，见4752)theory and models of chaotic systems(for chaos inflowing systems,see 4752)0547 非线性动力学系统和分岔(流体系统中的分岔，见4752)nonlinear dynamical systems and bifurcations(bifurcations in flowing systems,see 4752)0550 点阵理论和统计学;伊辛问题(7510H伊辛模型)lattice theory and statistics; Ising problems(7510HIsing models)0555 分形(流体系统中的分形，见4752)fractals (fractals in flowing systems,see 4752) 0560 输运过程:理论 transportprocesses:theory 0565 自组织系统 Self-organizedsystems0570 热力学(4460热力学过程;6400状态方程,相平衡和相变;6500凝聚物质的热性质 ; 化学热力学,见8260)thermodynamics(4460 thermodynamic processes;6400 equation s of state, phase equilibria andphase transitions; 6500 thermal properties ofcondensed matter;for chemical thermodynamics,see 8260)0570C 热力学函数及状态方程thermodynamic functions and equations of state0570F 相变:一般问题phase transitions: general aspects 0570J 临界点现象critical point phenomena0570L 非平衡热力学、不可逆过程(3430势能表面;8200物理化学)nonequilibrium thermodynamics, irreversibleprocesses(3430 potential energy surfaces, 8200physical chemistry)0580 经济物理学 Econophysics0590 统计物理学和热力学的其它论题other topics in statistical physics and thermodynamics0600 测量科学、普通实验室技术及测试设备系统Measurement science, general laboratorytechniques, and instrumentation systems0620 基本度量学 metrology 0620D 测量与误差理论measurement and error theory0620F 单位 units 0620H 测量标准和校正measurement standards and calibration 0620J 基本常数测定determination of fundamental constants 0630 基本变量测量measurement of basic variables0630C 空间变量测量(包括空间延伸的所有变量如:直径、重量、厚度、位移、表面拓扑学、粒子尺寸、弥散系统区)spatial variables measurement(inc.measurementof all variables extending in space e.g. diameter,weight, thickness, displacement , surfacetopography, particle size, area of dispersesystems)0630E 质量与密度的测量mass and density measurement0630F 时间与频率的测量(天文学方面的,见9570)time and frequency measurement(for astronomicalaspects see 9570)0630G 速度、加速度和转动测量(流速测量,见4780)velocity, acceleration and rotationmeasurement(for flow velocity measurement see4780)0630L 基本电磁变量测量(0750电学仪器和技术)measurement of basic electromagneticvariables(0750 electrical instruments andtechniques)0630M 机械变量测量(包括弹性模量，力，冲击，应变，应力，力矩和振动)(压力测量，见0630N；声学变量测量，见4385D；固体力学测量，见4630R；粘度测量，见4780；材料试验，8170)measurement of mechanical variables(inc.elasticmoduli,force,shock ,strain,stress,torque,andvibration)(for pressure measurement,see0630N;for acoustic variables measurement,see4385D;for measurement in the mechanics ofsolids, see 4630R;for viscosity measurement,see4780;for materials testing,see 8170)0630N 压力测量(真空测量，见0730D；高压技术，见0735)pressure measurement(for vacuum measurement,see 0730D;for high-pressure techniques, see0735)0650 数据处理和计算(0270计算技术;2980核信息处理;光学数据处理,存贮及检索, 见423 0;地球物理数据采集和存贮,见9365)data handling and computation(0270computational techniques; 2980 nuclearinformation processing;for optical dataprocessing , storage and retrieval see 4230; forgeophysical data acquisition and storage see9365)0650D 数据搜集、处理、记录、数据显示(含数显技术)data gathering, processing, and recording, datadisplays (including digital techniques)0650M 计算装置与技术computing devices and techniques0660 实验室技术 laboratorytechniques 0660E 样品制备 samplepreparation0660J 高速技术(微秒到微微秒) high　speed techniques (microsecond to picosecond)0660S 微检验装置、微定位器和切片机micromanipulators, micropositioners , and microtomes0660V 车间技术(焊接、机械加工、润滑作用和轴承等)workshop techniques ( welding, machining,lubrication, bearings, etc.)0660W 安全(2880辐射监测和防护;8760M辐射剂量测定法;8760P辐射防护)safety( 2880 radiation monitoring and protection,8760M radiation dosimetry, 8760P radiationprotection)0670 普通测试设备 generalinstrumentation 0670D 敏感元件和探测器sensing and detecting devices0670E 试验设备 testingequipment 0670H 显示、记录与指示器display, recording, and indicating instrument s0670M 换能器(电磁辐射换能器见0762;声换能器见4388;液流换能器见4780)transducers(for electromagnetic radiationtransducers see 0762; for acoustic transducers see4388; for flow transducers see 4780)0670T 伺服及控制装置servo and control devices0690 测量科学、普通实验室技术及测试设备系统中的其它论题other topics in measurement science, generallaboratory techniques and instrumentationsystems0700 物理学中普遍使用的专用测试设备与技术(各分支学科的专用测试设备与技术入各自的分支学科)specific instrumentation and techniques of generaluse in physics(within each subdiscipline forspecialized instrumentation and techniques)0710 机械仪器与测量方法(固体力学测量见4630R;材料试验见8170)mechanical instruments and measurementmethods(for measurement in the mechanics of solids, see 4630R; for materials testing, see 8170)0710C 微机械器件和系统(微光学器件和技术，见4283)micromechanical devices and systems (formicrooptical devices and technology,see 4283)0710F 隔振 vibrationisolation0710Y 其他机械仪器和技术(包括摆、陀螺仪、离心器)other mechanical instruments andtechniques(inc.pendulums,gyroscopes,centrifuges)0720 热仪器和技术(4450物质的热性质;4460热力学过程;热辐射的辐射度学和检测, 见 0760D和0762)thermal instruments and techniques(4450 thermalproperties of matter, 4460 thermodynamicprocesses;for radiometry and detection of thermalradiation see 0760D and 0762)0720D 温度测量 thermometry 0720F 量热学 calorimetry 0720H 加热炉 furnaces0720K 高温技术及测试设备;测高温术high　temperature techniques and instrumentation; pyrometry0720M 低温实验法 cryogenics 0725 测湿法 hygrometry0730 真空产生与真空技术(包括低于1个大气压的压力;稀薄气体动力学入4745;8115 G 真空淀积)vacuum production and techniques(inc.pressuresbelow 1atmosphere; 4745 rarefied gas dynamics;8115G vacuum deposition)0730B 排空能力、除气、剩余气体evacuating power, degasification, residual gas 0730C 真空泵 vacuumpumps 0730D 真空计 vacuummeters 0730G 真空设备及试验方法vacuum apparatus and testing methods0730K 辅助设备、器件及材料auxiliary apparatus, hardware and materials0735 高压产生与技术(包括大于1个大气压的压力)high pressure production and techniques(inc.pressures above 1 atmosphere)0750 电学仪器及技术electrical instruments and techniques 0755 磁测量仪器及技术magnetic instruments and techniques0758 磁共振谱仪、辅助仪器和技术(6116N电子顺磁共振和核磁共振测定)magnetic resonance spectrometers, auxiliaryinstruments and techniques(6116N EPR and NMRdeterminations)0760 光学仪器和技术(辐射探测见0762;光谱学和光谱计见0765;全息术见4240;光源和标准见4272;光学透镜和反射系统见4278;光学器件、技术和应用见4280;光学试验和加工技术见4285;辐射谱仪和光谱技术见2930;辐射测量、检测和计数见2970)optical instruments and techniques(for radiationdetection, see 0762; for spectroscopy andspectrometers, see 0765; for holography, see4240; for optical sources and standards, see 4272;for optical lens and mirror systems, see 4278; foroptical devices , techniques and applications, see4280; for optical testing and workshop techniques,see 4285; for radiation spectrometers andspectroscopic techniques, see 29 30; for radiationmeasurement, detection and counting, see 2970)0760D 光度学和辐射度学(包括色度学,辐射探测入0762)photometry and radio metry(inc.colorimetry;0762detection of radiation)0760F 偏振测量术与椭园偏振测量术 polarimetryandellipsometry0760H 折射测量术与反射测量术 refractometryandreflectometry 0760L 干涉量度学 interferometry 0760P 光学显微术 opticalmicroscopy0762 辐射探测(测辐射热计、光电管、红外波与亚毫米波探测)detection of radiation (bolometers, photoelectriccells, IR. and submillimetre waves detection)0765 光谱学与光谱计(包括光声谱术) optical spectroscopy and spectrometers(inc.photoacoustic spectroscopy)0765E 紫外和可见光谱学与光谱仪UV and visible spectroscopy and spectrometers 0765G 红外光谱学与光谱仪IR spectroscopy and spectrometers0768 照相术、照相仪器与技术(光敏材料参见4270;照相过程的化学参见8250)photography, photographic instruments andtechniques(for light sensitive materials see also4270 for chemistry of photographic process seealso 8250)0775 质谱仪与质谱测定技术(质谱化学分析见8280)mass spectrometers and m ass spectrometrytechniques(for mass spectroscopic chemicalanalysis, see 8280)0777 粒子束的产生与处理;(2925基本粒子和核物理中的粒子源和靶;4180粒子束和粒子光学)particle beam production and handling;(2925particle sources and targets in elementary　particle and nuclear physics, 4180 particle beamsand particle optics)0779 扫描探针显微术及其相关技术(包括扫描隧道显微术，原子力显微术、磁力显微术，摩擦力显微术，和近场扫描光学显微术，(结构测定方面，参见6116P)scanning prob e microscopy and relatedtechniques(inc.scanning tunnellingmicroscopy,atomic force microscopy,magneticforce microscopy,friction force microscopy,andnear　field scanning opticalmicroscopy)(structure determination aspects, seealso 6116P)0780 电子与离子显微镜及其技术(6116D凝聚物质中的电子显微术;6116F凝聚物质中的场离子显微术)electron and ion microscopes andtechniques(6116D in condensed matter electronmicroscopy, 6116F field ion microscopy)0781 电子和离子谱仪及其相关技术(参见2930辐射谱仪和光谱技术)electron and ion spectrometers and relatedtechniques(see also 2930 radiation spectrometersan d spectroscopic techniques)0785 X射线与γ射线仪器与技术(包括穆斯堡尔谱仪和技术)X-ray, gamma-ray instruments and techniques(inc.Moessbauer spectrometers and technique s)0788 粒子干涉量度学和中子仪器(粒子束的产生与处理，参见0777;中子谱仪，参见 2930H ，原子干涉量度学，参见3580粒子光学，参见4180)particle interferometry and neutroninstrumentation(for particle beam production andhandling,see 0777;for neutron spectrometers,seealso 2930H;for atomic interferometry,see also3580;for particle optics,see also 4180)0790 专用设备中的其它论题other topics in specialised instrumentation1000 基本粒子物理与场(宇宙线见9440;高能实验技术和设备见 2900)THE PHYSICS OF ELEMENTARY PARTICLESAND FIELDS(for cosmic rays ,see 9440;for highenergy experimental techniques andinstrumentation, see 2900)1100 场和粒子的一般理论(0365量子力学;0370量子场论;0380散射的一般理论)general theory of fields and particles(0365quantum mechanics, 0370 theory of quantizedfields, 0380 general theory of scattering)1110 场论 fieldtheory 1110C 公理法 axiomaticapproach 1110E 拉氏函数和哈密顿函数法Lagrangian and Hamiltonian approach1110G 重正化 renormalization 1110J 渐近问题与特性asymptotic problems and properties1110L 非线性或非局域理论及模型nonlinear or nonlocal theories and models1110M 史文格源理论 Schwingersourcetheory 1110N 规范场论gauge field theories1110Q 相对论性波动方程relativistic wave equations1110S 束缚与非稳定态;贝特-沙耳皮特方程bound and unstable states; Bethe-Salpeterequations1110W 有限温度场论finite temperature field theory1117 弦理论和其他扩展物质理论(包括超弦和膜)theories of strings and other extendedobjects(inc.superstrings and membranes)1120 S-矩阵论 S-matrixtheory 1120D 散射矩阵和微扰论scattering matrix and perturbation theory1120F 色散关系和S矩阵的分析特性dispersion relations and analytic properties of the S-matrix1130 对称和守恒定律(0220群论) symmetry and conservation laws(0220 group theory)1130C 洛伦兹与庞加莱不变性Lorentz and Poincare invariance1130E 电荷共轭、宇称、时间反演和其它分立对称charge conjugation, parity, time reversal and otherdiscrete symmetries1130J SU(2)和SU(3)对称SU(2) and SU(3) symmetries1130K SU(4)对称 SU(4)symmetry 1130L 其他内部对称和高度对称other internal and higher symmetries1130N 非线性对称和动力学对称性(谱生成对称)nonlinear and dynamical symmetries (spectrum　generating symmetries)1130P 超对称 supersymmetry1130Q 自发性对称破缺spontaneous symmetry breaking1130R 手征对称 chiralsymmetries 1140 流及其特性currents and their properties1140D 流的一般理论general theory of currents1140F 流代数的拉格朗日算法Lagrangian approach to current algebras1140H 部分守恒轴矢量流partially conserved axial　vector currents 1150 色散关系与求和定则dispersion relations and sum rules1150E n/d法 n/dmethod 1150G 靴襻 bootstraps 1150J 交叉对称 crossingsymmetries 1150L 求和定则 sumrules1150N 多变量色散关系(包括曼德尔斯坦表象)multivariable dispersion relations(inc.Mandelstamrepresentation)1160 复合角动量;雷其(理论)体系(0380一般散射理论;1240强相互作用中的复合角动量)complex angular momentum; Reggeformalism(0380 general theory of scattering, 1240in strong interactions)1180 相对论性散射理论(0380一般散射理论)relativistic scattering theory (0380 general theoryof scattering)1180C 运动特性(螺旋性和不变振幅、运动奇异性等)kinematical properties (helicity and invariantamplitudes, kinematic singularities, etc.)1180E 部分波分析 partial　wave analysis1180F 近似法(程函近似法,变分原理等) approximations (eikonal approximation, variational principles, etc)1180G 多道散射 multichannelscattering 1180J 多体散射和Faddeev方程Many-body scattering and Faddeev equation 1180L 多次散射 multiplescattering 1190 一般场论和粒子理论的其它论题other topics in general field and particle theory1200 具体理论和相互作用模型;粒子分类系统specific theories and interaction models; particlesystematics1210 统一场论和模型unified field theories and models1210B 电弱理论 electroweaktheories 1210C 统一化标准模型standard model of unification1210D 标准模型以外的统一模型(包括GUTS，颜色模型和SUSY模型)unified models beyond the standardmodel(inc.GUTS,technicolour and SUSY models)1220 电磁相互作用模型models of electromagnetic interactions1220D 量子电动力学的具体计算和极限specific calculations and limits of quantum electrodynamics1220F 量子电动力学的实验检验experimental tests of quantum electrodynamics 1225 引力相互作用模型(0460引力的量models for gravitational interactions(0460子论) quantum theory of gravitation)1230 弱相互作用模型models of weak interactions1230C 中子流 neutralcurrents 1230E 中间玻色子 intermediatebosons 1235 粒子的复合模型composite models of particles1235C 量子色动力学的一般特性(动力学,禁闭等)general properties of quantum chromodynamics(dynamics, confinement, etc.)1235E 量子色动力学在粒子特性和反应中的应用applications of quantum chromodynamics toparticle properties and reactions1235H 粒子的结构和反应的唯象复合模型(部分子模型,口袋模型等)phenomenological composite models of particlestructure and reactions (partons, bags, etc.)1235K 其它复合模型(包括复合夸克模型和轻子模型)other composite models( posite quarksand leptons)1240 强相互作用模型models of strong interactions1240E 统计模型 statisticalmodels1240F 靴襻模型 bootstrapmodels1240H 二重性和双关模型duality and dual models1240K 强子分类方案 hadronclassificationschemes1240M 复合角动量平面;雷其极点和割线(雷其子)(1160复合角动量,雷其体系的一般理论)complex angular momentum plane; Regge polesand cuts (Reggeons)(1160 for general theory)1240P 吸收模型,光学模型和程函模型(衍射和衍射生成模型见1240S)absorptive, optical, and eikonal models(fordiffraction and diffractive production models, see1240S)1240Q 势模型 potentialmodels1240R 边缘碰撞模型(一个或多个粒子交换) peripheral models (one or more particle exchange)1240S 多重边缘碰撞模型和多雷其模型(包括衍射和衍射生成模型)multiperipheral and multi　Reggemodels(inc.diffraction and diffractive productionmodels)1240V 矢量介子优势 Vector-mesondominance 1270 强子质量公式hadron mass formulas1290 其它各种理论设想与模型miscellaneous theoretical ideas and models1300 具体基本粒子反应和唯象论specific elementary particle reactions and phenomenology1310 轻子间的弱相互作用和电磁相互作用weak and electromagnetic interactions of leptons1315 中微子相互作用(包括宇宙射线相互作用)neutrino interactions(inc.interactions involvingcosmic rays)1320 介子的轻子与半轻子衰变leptonic and semileptonic decays of mesons1320C π衰变 pidecays1320E K衰变 Kdecays1320G Ψ/J介子、Υ介子、Φ介子psi/J, upsilon, phi mesons1320H B介子轻子/半轻子衰变 Bmesonleptonic/semileptonicdecays 1320I f介子轻子/半轻子衰变 fmesonleptonic/semileptonicdecays 1320J 其它介子衰变other meson decays1325 介子的强子衰变 hadronicdecaysofmesons 1330 重子的衰变 decaysofbaryons1330C 轻子与半轻子衰变leptonic and semileptonic decays1330E 强子衰变 hadronicdecays 1335 轻子的衰变 decaysofleptons1338 中间玻色子和希格斯玻色子的衰变decays of intermediate and Higgs Bosons1340 电磁过程与特性electromagnetic processes and properties1340D 电磁质量差electromagnetic mass differences1340F 电磁形状因子、电矩和磁矩electromagnetic form factors; electric and magnetic moments1340H 电磁衰变 electromagneticdecays1340K 强相互作用和弱相互作用过程的电磁修正electromagnetic corrections to strong and weakinteraction processes1360 光子及带电轻子与强子的相互作用(中微子相互作用见1315)photon and charged　lepton interactions withhadrons(for neutrino interactions, see 1315)1360F 弹性散射与康普顿散射elastic and Compton scattering1360H 总截面和单举(反应)截面(包括深度非弹性过程)total and inclusive crosssections(inc.deep-inelastic processes)1360K 介子产生 mesonproduction 1360M 介子共振产生 Meson-resonanceproduction 1360P 重子和重子共振产生baryon and baryon resonance production1365 电子-正电子碰撞产生强子hadron production by electron-positron collisions1375 强子诱发的低能和中能反应及散射(能量≤10GeV见1385)Hadron-induced low　energy and intermediate　energy reactions and scattering, energy ≤10GeV( for higher energies, see 1385)1375C 核子-核子相互作用,包括反核子和氘核等(能量≤10GeV;核中的核子-核子相互作用见2130)Nucleon-nucleon interactions, includingantinucleon, deuteron, etc. (energy ≤10GeV)(for n-n interactions in nuclei, see 2130)1375E 超子-核子相互作用(能量≤10GeV)Hyperon-nucleon interactions (energy ≤10 GeV)1375G π介子-重子相互作用(能量≤10GeV) Pion-baryon interactions (energy ≤10 GeV)1375J K介子-重子相互作用(能量≤10GeV) Kaon-baryon interactions (energy ≤10 GeV)1375L 介子-介子相互作用(能量≤10GeV)Meson-meson interactions (energy ≤10 GeV) 1380 光子-光子相互作用和散射 Photon-photon interactions and scattering1385 强子诱发的高能和超高能相互作用(能量>10GeV)(低能情况见1375) Hadron-induced high-energy and super-high-energy interactions, energy > 10GeV(for low energies, see 1375)1385D 弹性散射(能量=10GeV) elastic scattering (energy = 10 GeV)1385F非弹性散射、双粒子终态(能量>10GeV) inelastic scattering, two-particle final states(energy > 10 GeV) 1385H 非弹性散射、多粒子终态(能量>10GeV) inelastic scattering, many-particle final states(energy>10GeV)1385K 单举反应,包括总截面(能量>10GeV) inclusive reactions, including total cross sections,(energy > 10 GeV)1385M 宇宙射线相互作用(9440宇宙线) cosmic ray interactions(9440 cosmic rays)1385N 强子诱发的高能相互作用(能量>1TeV) hadron induced very high energy interactions(energy>1 TeV)1387大Q2基本粒子相互作用中的射流jets in large-Q2 elementary particle interactions 1388相互作用和散射中的极化 polarisation in interactions and scattering 1390基本粒子的具体反应及唯象论的其它论题 other topics in specific reactions and phenomenology of elementary particles 1400具体粒子的性质与共振 properties of specific particles and resonances 1420 重子与重子共振(包括反粒子) baryons and baryon resonances(inc.antiparticles)1420C 中子 neutrons1420E 质子 protons1420G s =0时的重子共振baryon resonances with s=0 1420J超子和超子共振 hyperons and hyperon resonances 1420P双重子 dibaryons1440 介子和介子共振 mesons and meson resonances 1440D π介子 pi mesons1440F K 介子 K mesons1440K Ρ介子、Ω介子和η介子rho, omega, and eta mesons 1440L d 介子和F 介子d and F mesons 1440N Ψ/J 介子、Υ介子、Φ介子psi/J, upsilon, phi mesons 1440P其它介子 other mesons 1460 轻子 leptons1460C 电子和正电子 electrons and positrons 1460E μ介子 muons1460G 中微子 neutrinos1460J重轻子 heavy leptons 1480 其它粒子和假设粒子 other and hypothetical particles1480A 光子 photons1480D 夸克和胶子 quarksandgluons 1480F 中间玻色子 intermediateBosons 1480H 磁单极子 magneticmonopoles1480J 超对称粒子(包括标量粒子，超粒子和超离子)Supersymmetric particles(inc.scalarparticles,superparticles and superions)1480K 其它(包括快子) others(inc.tachyons)2000 核物理学 NUCLEARPHYSICS 2100 核结构 nuclearstructure2110 核的一般和平均性质;核能级性质(按质量范围分类的具体核的性质见2700)general and average properties of nuclei;properties of nuclear energy levels(for propertiesof specific nuclei listed by mass ranges, see 2700)2110D 结合能和质量binding energy and masses2110F 形状、电荷、半径和形状因子shape, charge, radius and form factor s2110H 自旋、宇称和同位旋spin, parity, and isobaric spin2110J 谱因子 spectroscopicfactors 2110K 电磁矩 electromagneticmoments 2110M 能级密度和结构level density and structure2110P 单粒子能级结构single particle structure in levels2110R 集团能级结构(包括旋转能带) collective structure in levels(inc.rotational bands) 2110S 库仑效应 Coulombeffects2130 核力(1375C核子-核子相互作用) nuclear forces(1375C nucleon-nucleon interactions)2140 少核子系统 Few-nucleonsystems2160 核结构模型与方法(强子的原子和分子见3610)nuclear　structure models and methods(forhadronic atoms and molecules, see 3610)2160C 壳层模型 shellmodel2160E 集体模型 collectivemodels 2160F 群论模型models based on group theory2160G 集团模型 clustermodels 2160J 哈特里-福克和随机-相位近似Hartree-Fock and random-phase approximations 2165 核物质 nuclearmatter 2180 超核 hypernuclei 2190 核结构的其它论题other topics in nuclear structure2300 放射性和电磁跃迁(8255放射化学)radioactivity and electromagnetic transitions(8255 radiochemistry)2320 电磁跃迁 electromagnetictransitions 2320C 寿命和跃迁几率lifetimes and transition probabilities2320E 角分布和校正测量angular distribution and correlation measurements2320G 多极混合比率 multipolemixingratios 2320J 多极矩阵元素 multipolematrixelements 2320L γ跃迁和能级gamma transitions and level energies2320N 内转换和核外效应internal conversion and extranuclear effects 2320Q 核共振荧光nuclear resonance fluorescence2340 β衰变;电子与μ子俘获beta decay; electron and muon capture2340B 弱相互作用和β衰变的轻子特性weak interaction and lepton aspects of beta decay2340H 核矩阵元和从β衰变推断核结构nuclear matrix elements and nuclear structure inferred from beta decay2360 α衰变 alphadecay 2390 核衰变和放射性的其它论题other topics in nuclear decay and radioactivity 2400 核反应和散射:总论nuclear reactions and scattering:general2410 核反应和散射模型与方法nuclear reaction and scattering models and methods2410D 耦合道和多体论方法coupled　channel and many　body　theory methods2410F 平面和扭曲波玻恩近似法Plane- and distorted-wave Born approximations 2410H 光学模型和衍射模型optical and diffraction models2430 共振反应与散射resonance reactions and scattering2430C 巨共振 giantresonances 2430F 同位旋相似共振 isobaricanalogresonances 2450 直接反应 directreactions 2460 统计理论和涨落statistical theory and fluctuations2470 反应和散射中的极化polarization in reactions and scattering2475 裂变的一般性质general properties of fission2485 原子核和核形成过程的夸克模型quark models in nuclei and nuclear processes2490 核反应和散射的其它论题:一般问题other topics in nuclear reactions and scattering:general2500 核反应和散射:具体反应nuclear reactions and scattering:specific reactions2510 少核子系统的核反应与散射nuclear reactions and scattering involving few-nucleon systems2520 光致核反应和光子散射 photonuclearreactions and photon scattering 2530 轻子诱发反应与散射Lepton-induced reactions and scattering 2530C 电子和正电子反应与散射electron and positron reactions and scattering 2530E μ介子反应和散射muon reactions and scattering2530G 中微子反应和散射neutrino reactions and scattering。

量子力学复习题

Ex.1 已知一维粒子状态波函数为
(ra2x2
i 2
t
求归一化的波函数，粒子的几率分布，粒子在何处出
现的几率最大。
Solve:
(1).求归一化的波函数
2
(r,t) dx
A2
ea2x2 dx
A2
归一化常数
1/ 2
A a/
1
a2
归一化的波函数
1/ 2 1a2x2 i t
l0
个波函数，即 En的简并度为n2
Ex. n = 2 时，E2 是4度简并的，对应的波函数有
200 , 211 , 210 , 211
对库仑简场l、并中m ，电这子是的库能仑级场E所n只特与有的n有。关，与 (l, m无) 关，
3.6 算符与力学量的关系（续５）
Chap.3 The Dynamical variable in Quantum Mechanism
（1）若两个厄米算符有共同本征态，它们是否就彼此对易。（2）若两个厄米算符不对易，是否一定就没有共同本征态。（3）若两个厄米算符对易，是否在所有态下它们都同时具有确定值。
（4）若 [ Aˆ, Bˆ ]=常数， Aˆ 和 Bˆ能否有共同本征态。（5）角动量分量 Lˆx和 Lˆ能y 否有共同本征态。
§4.1 态的表象（续２）
Chap.4 The representation for the states and dynamical variable
命题若 (r,t)是归一化波函数，则 C(P,t也) 归一。
证 1 *(x,t) (x,t)dx
[ C(p,t) p(x)dp] * [ C(p,t) p(x)dp]dx
Solve 选择动量表象:

量子力学第二版周世勋1PDF

1 Quantum mechanism Quantum mechanism 宝鸡文理学院物理与信息技术系1.《量子力学教程》曾谨言著科学出版社2003年第一版普通高等教育十五国家级规划教材 2.《量子力学导论》曾谨言著北京大学出版社 1998年第二版 3.《量子力学导论》熊钰庆主编广东高等教育出版社 2000年第一版《量子力学教程》周世勋编高等教育出版社参考书及学习网站4.《量子力学基础》关洪高等教育出版社 1999年第一版 5.《量子力学》汪德新湖北科学技术出版社出版 2000年第一版 6.《量子力学教程习题剖析》孙婷雅编科学出版社出版 2004年第一版 7. 宝鸡文理学院陕西省精品课程《量子力学》http://218.195.112.45/jpkc/liangzi/kc_web/ Content Content 第一章绪论Ch1. The basic concepts of quantum mechanism 第二章波函数和薛定谔方程Ch2. The wave function and Schr??dinger’s equation 第三章量子力学中的力学量Ch3. The Dynamical variable in Quantum Mechanism 第四章态和力学量的表象Ch4. The representation of the states and operators 第五章微扰理论Ch5. Perturbation theory第六章散射Ch6. The general theory of scattering 第七章自旋与全同粒子Ch7. Spin and identity of particles The birth of quantum mechanismThe birth of quantum mechanism Chap.1.绪论The birth of quantum mechanism Chap.1.绪论The birth of quantum mechanism 6 1.1 经典物理学的困难The difficult in classical physics 1.2 光的波粒二象性The duality of light between wave and particle 1.3 微粒的波粒二象性The duality of small particles between wave and particle Chap.1.绪论The birth of quantum mechanism Chap.1.绪论The birth of quantum mechanism 7 近几十年来在不同领域相继发现了宏观量子效应如超导现象超流现象乃至一些天体现象表明宏观世界的物质运动也遵循量子力学规律人们所熟知的经典力学规律只是量子力学规律在特定条件下的一个近似。

埃伦费斯定理

It is often said that Ehrenfest’s theorem shows that expectation values obey the classical dynamical laws. This slogan is not quite true. In particular, the expectation value of position does not necessarily obey Newton’s second law. A true version of Newton’s second law for the expectation value would read
Harmonic Oscillator: Deﬁnitions, the Hamiltonian We now begin a survey of key properties of one of the workhorse models of quantum
mechanics: the simple harmonic oscillator (SHO). This model is useful because it is analytically quite tractable, it illustrates a wide variety of quantum mechanical features both
and use the time independence of the state vector to obtain (exercise)
d2 dt2 X (t) = F (t), where F is the force. This result is Ehrenfest’s theorem.

人工智能英汉

人工智能英汉Aβα-Pruning, βα-剪枝, (2) Acceleration Coefficient, 加速系数, (8) Activation Function, 激活函数, (4) Adaptive Linear Neuron, 自适应线性神经元,(4)Adenine, 腺嘌呤, (11)Agent, 智能体, (6)Agent Communication Language, 智能体通信语言, (11)Agent-Oriented Programming, 面向智能体的程序设计, (6)Agglomerative Hierarchical Clustering, 凝聚层次聚类, (5)Analogism, 类比推理, (5)And/Or Graph, 与或图, (2)Ant Colony Optimization (ACO), 蚁群优化算法, (8)Ant Colony System (ACS), 蚁群系统, (8) Ant-Cycle Model, 蚁周模型, (8)Ant-Density Model, 蚁密模型, (8)Ant-Quantity Model, 蚁量模型, (8)Ant Systems, 蚂蚁系统, (8)Applied Artificial Intelligence, 应用人工智能, (1)Approximate Nondeterministic Tree Search (ANTS), 近似非确定树搜索, (8) Artificial Ant, 人工蚂蚁, (8)Artificial Intelligence (AI), 人工智能, (1) Artificial Neural Network (ANN), 人工神经网络, (1), (3)Artificial Neural System, 人工神经系统，(3) Artificial Neuron, 人工神经元, (3) Associative Memory, 联想记忆, (4) Asynchronous Mode, 异步模式, (4) Attractor, 吸引子, (4)Automatic Theorem Proving, 自动定理证明,(1)Automatic Programming, 自动程序设计, (1) Average Reward, 平均收益, (6) Axon, 轴突, (4)Axon Hillock, 轴突丘, (4)BBackward Chain Reasoning, 逆向推理, (3) Bayesian Belief Network, 贝叶斯信念网, (5) Bayesian Decision, 贝叶斯决策, (3) Bayesian Learning, 贝叶斯学习, (5) Bayesian Network贝叶斯网, (5)Bayesian Rule, 贝叶斯规则, (3)Bayesian Statistics, 贝叶斯统计学, (3) Biconditional, 双条件, (3)Bi-Directional Reasoning, 双向推理, (3) Biological Neuron, 生物神经元, (4) Biological Neural System, 生物神经系统, (4) Blackboard System, 黑板系统, (8)Blind Search, 盲目搜索, (2)Boltzmann Machine, 波尔兹曼机, (3) Boltzmann-Gibbs Distribution, 波尔兹曼-吉布斯分布, (3)Bottom-Up, 自下而上, (4)Building Block Hypotheses, 构造块假说, (7) CCell Body, 细胞体, (3)Cell Membrane, 细胞膜, (3)Cell Nucleus, 细胞核, (3)Certainty Factor, 可信度, (3)Child Machine, 婴儿机器, (1)Chinese Room, 中文屋, (1) Chromosome, 染色体, (6)Class-conditional Probability, 类条件概率,(3), (5)Classifier System, 分类系统, (6)Clause, 子句, (3)Cluster, 簇, (5)Clustering Analysis, 聚类分析, (5) Cognitive Science, 认知科学, (1) Combination Function, 整合函数, (4) Combinatorial Optimization, 组合优化, (2) Competitive Learning, 竞争学习, (4) Complementary Base, 互补碱基, (11) Computer Games, 计算机博弈, (1) Computer Vision, 计算机视觉, (1)Conflict Resolution, 冲突消解, (3) Conjunction, 合取, (3)Conjunctive Normal Form (CNF), 合取范式,(3)Collapse, 坍缩, (11)Connectionism, 连接主义, (3) Connective, 连接词, (3)Content Addressable Memory, 联想记忆, (4) Control Policy, 控制策略, (6)Crossover, 交叉, (7)Cytosine, 胞嘧啶, (11)DData Mining, 数据挖掘, (1)Decision Tree, 决策树, (5) Decoherence, 消相干, (11)Deduction, 演绎, (3)Default Reasoning, 默认推理（缺省推理）,(3)Defining Length, 定义长度, (7)Rule (Delta Rule), 德尔塔规则, 18(3) Deliberative Agent, 慎思型智能体, (6) Dempster-Shafer Theory, 证据理论, (3) Dendrites, 树突, (4)Deoxyribonucleic Acid (DNA), 脱氧核糖核酸, (6), (11)Disjunction, 析取, (3)Distributed Artificial Intelligence (DAI), 分布式人工智能, (1)Distributed Expert Systems, 分布式专家系统,(9)Divisive Hierarchical Clustering, 分裂层次聚类, (5)DNA Computer, DNA计算机, (11)DNA Computing, DNA计算, (11) Discounted Cumulative Reward, 累计折扣收益, (6)Domain Expert, 领域专家, (10) Dominance Operation, 显性操作, (7) Double Helix, 双螺旋结构, (11)Dynamical Network, 动态网络, (3)E8-Puzzle Problem, 八数码问题, (2) Eletro-Optical Hybrid Computer, 光电混合机, (11)Elitist strategy for ant systems (EAS), 精化蚂蚁系统, (8)Energy Function, 能量函数, (3) Entailment, 永真蕴含, (3) Entanglement, 纠缠, (11)Entropy, 熵, (5)Equivalence, 等价式, (3)Error Back-Propagation, 误差反向传播, (4) Evaluation Function, 评估函数, (6) Evidence Theory, 证据理论, (3) Evolution, 进化, (7)Evolution Strategies (ES), 进化策略, (7) Evolutionary Algorithms (EA), 进化算法, (7) Evolutionary Computation (EC), 进化计算,(7)Evolutionary Programming (EP), 进化规划,(7)Existential Quantification, 存在量词, (3) Expert System, 专家系统, (1)Expert System Shell, 专家系统外壳, (9) Explanation-Based Learning, 解释学习, (5) Explanation Facility, 解释机构, (9)FFactoring, 因子分解, (11)Feedback Network, 反馈型网络, (4) Feedforward Network, 前馈型网络, (1) Feasible Solution, 可行解, (2)Finite Horizon Reward, 横向有限收益, (6) First-order Logic, 一阶谓词逻辑, (3) Fitness, 适应度, (7)Forward Chain Reasoning, 正向推理, (3) Frame Problem, 框架问题, (1)Framework Theory, 框架理论, (3)Free-Space Optical Interconnect, 自由空间光互连, (11)Fuzziness, 模糊性, (3)Fuzzy Logic, 模糊逻辑, (3)Fuzzy Reasoning, 模糊推理, (3)Fuzzy Relation, 模糊关系, (3)Fuzzy Set, 模糊集, (3)GGame Theory, 博弈论, (8)Gene, 基因, (7)Generation, 代, (6)Genetic Algorithms, 遗传算法, (7)Genetic Programming, 遗传规划（遗传编程）,(7)Global Search, 全局搜索, (2)Gradient Descent, 梯度下降, (4)Graph Search, 图搜索, (2)Group Rationality, 群体理性, (8) Guanine, 鸟嘌呤, (11)HHanoi Problem, 梵塔问题, (2)Hebbrian Learning, 赫伯学习, (4)Heuristic Information, 启发式信息, (2) Heuristic Search, 启发式搜索, (2)Hidden Layer, 隐含层, (4)Hierarchical Clustering, 层次聚类, (5) Holographic Memory, 全息存储, (11) Hopfield Network, 霍普菲尔德网络, (4) Hybrid Agent, 混合型智能体, (6)Hype-Cube Framework, 超立方体框架, (8)IImplication, 蕴含, (3)Implicit Parallelism, 隐并行性, (7) Individual, 个体, (6)Individual Rationality, 个体理性, (8) Induction, 归纳, (3)Inductive Learning, 归纳学习, (5) Inference Engine, 推理机, (9)Information Gain, 信息增益, (3)Input Layer, 输入层, (4)Interpolation, 插值, (4)Intelligence, 智能, (1)Intelligent Control, 智能控制, (1) Intelligent Decision Supporting System (IDSS), 智能决策支持系统，(1) Inversion Operation, 倒位操作, (7)JJoint Probability Distribution, 联合概率分布,(5) KK-means, K-均值, (5)K-medoids, K-中心点, (3)Knowledge, 知识, (3)Knowledge Acquisition, 知识获取, (9) Knowledge Base, 知识库, (9)Knowledge Discovery, 知识发现, (1) Knowledge Engineering, 知识工程, (1) Knowledge Engineer, 知识工程师, (9) Knowledge Engineering Language, 知识工程语言, (9)Knowledge Interchange Format (KIF), 知识交换格式, (8)Knowledge Query and ManipulationLanguage (KQML), 知识查询与操纵语言，(8)Knowledge Representation, 知识表示, (3)LLearning, 学习, (3)Learning by Analog, 类比学习, (5) Learning Factor, 学习因子, (8)Learning from Instruction, 指导式学习, (5) Learning Rate, 学习率, (6)Least Mean Squared (LSM), 最小均方误差,(4)Linear Function, 线性函数, (3)List Processing Language (LISP), 表处理语言, (10)Literal, 文字, (3)Local Search, 局部搜索, (2)Logic, 逻辑, (3)Lyapunov Theorem, 李亚普罗夫定理, (4) Lyapunov Function, 李亚普罗夫函数, (4)MMachine Learning, 机器学习, (1), (5) Markov Decision Process (MDP), 马尔科夫决策过程, (6)Markov Chain Model, 马尔科夫链模型, (7) Maximum A Posteriori (MAP), 极大后验概率估计, (5)Maxmin Search, 极大极小搜索, (2)MAX-MIN Ant Systems (MMAS), 最大最小蚂蚁系统, (8)Membership, 隶属度, (3)Membership Function, 隶属函数, (3) Metaheuristic Search, 元启发式搜索, (2) Metagame Theory, 元博弈理论, (8) Mexican Hat Function, 墨西哥草帽函数, (4) Migration Operation, 迁移操作, (7) Minimum Description Length (MDL), 最小描述长度, (5)Minimum Squared Error (MSE), 最小二乘法,(4)Mobile Agent, 移动智能体, (6)Model-based Methods, 基于模型的方法, (6) Model-free Methods, 模型无关方法, (6) Modern Heuristic Search, 现代启发式搜索,(2)Monotonic Reasoning, 单调推理, (3)Most General Unification (MGU), 最一般合一, (3)Multi-Agent Systems, 多智能体系统, (8) Multi-Layer Perceptron, 多层感知器, (4) Mutation, 突变, (6)Myelin Sheath, 髓鞘, (4)(μ+1)-ES, (μ+1) -进化规划, (7)(μ+λ)-ES, (μ+λ) -进化规划, (7) (μ,λ)-ES, (μ,λ) -进化规划, (7)NNaïve Bayesian Classifiers, 朴素贝叶斯分类器, (5)Natural Deduction, 自然演绎推理, (3) Natural Language Processing, 自然语言处理,(1)Negation, 否定, (3)Network Architecture, 网络结构, (6)Neural Cell, 神经细胞, (4)Neural Optimization, 神经优化, (4) Neuron, 神经元, (4)Neuron Computing, 神经计算, (4)Neuron Computation, 神经计算, (4)Neuron Computer, 神经计算机, (4) Niche Operation, 生态操作, (7) Nitrogenous base, 碱基, (11)Non-Linear Dynamical System, 非线性动力系统, (4)Non-Monotonic Reasoning, 非单调推理, (3) Nouvelle Artificial Intelligence, 行为智能,(6)OOccam’s Razor, 奥坎姆剃刀, (5)(1+1)-ES, (1+1) -进化规划, (7)Optical Computation, 光计算, (11)Optical Computing, 光计算, (11)Optical Computer, 光计算机, (11)Optical Fiber, 光纤, (11)Optical Waveguide, 光波导, (11)Optical Interconnect, 光互连, (11) Optimization, 优化, (2)Optimal Solution, 最优解, (2)Orthogonal Sum, 正交和, (3)Output Layer, 输出层, (4)Outer Product, 外积法, 23(4)PPanmictic Recombination, 混杂重组, (7) Particle, 粒子, (8)Particle Swarm, 粒子群, (8)Particle Swarm Optimization (PSO), 粒子群优化算法, (8)Partition Clustering, 划分聚类, (5) Partitioning Around Medoids, K-中心点, (3) Pattern Recognition, 模式识别, (1) Perceptron, 感知器, (4)Pheromone, 信息素, (8)Physical Symbol System Hypothesis, 物理符号系统假设, (1)Plausibility Function, 不可驳斥函数（似然函数）, (3)Population, 物种群体, (6)Posterior Probability, 后验概率, (3)Priori Probability, 先验概率, (3), (5) Probability, 随机性, (3)Probabilistic Reasoning, 概率推理, (3) Probability Assignment Function, 概率分配函数, (3)Problem Solving, 问题求解, (2)Problem Reduction, 问题归约, (2)Problem Decomposition, 问题分解, (2) Problem Transformation, 问题变换, (2) Product Rule, 产生式规则, (3)Product System, 产生式系统, (3) Programming in Logic (PROLOG), 逻辑编程, (10)Proposition, 命题, (3)Propositional Logic, 命题逻辑, (3)Pure Optical Computer, 全光计算机, (11)QQ-Function, Q-函数, (6)Q-learning, Q-学习, (6)Quantifier, 量词, (3)Quantum Circuit, 量子电路, (11)Quantum Fourier Transform, 量子傅立叶变换, (11)Quantum Gate, 量子门, (11)Quantum Mechanics, 量子力学, (11) Quantum Parallelism, 量子并行性, (11) Qubit, 量子比特, (11)RRadial Basis Function (RBF), 径向基函数,(4)Rank based ant systems (ASrank), 基于排列的蚂蚁系统, (8)Reactive Agent, 反应型智能体, (6) Recombination, 重组, (6)Recurrent Network, 循环网络, (3) Reinforcement Learning, 强化学习, (3) Resolution, 归结, (3)Resolution Proof, 归结反演, (3) Resolution Strategy, 归结策略, (3) Reasoning, 推理, (3)Reward Function, 奖励函数, (6) Robotics, 机器人学, (1)Rote Learning, 机械式学习, (5)SSchema Theorem, 模板定理, (6) Search, 搜索, (2)Selection, 选择, (7)Self-organizing Maps, 自组织特征映射, (4) Semantic Network, 语义网络, (3)Sexual Differentiation, 性别区分, (7) Shor’s algorithm, 绍尔算法, (11)Sigmoid Function, Sigmoid 函数（S型函数）,(4)Signal Function, 信号函数, (3)Situated Artificial Intelligence, 现场式人工智能, (1)Spatial Light Modulator (SLM), 空间光调制器, (11)Speech Act Theory, 言语行为理论, (8) Stable State, 稳定状态, (4)Stability Analysis, 稳定性分析, (4)State Space, 状态空间, (2)State Transfer Function, 状态转移函数,(6)Substitution, 置换, (3)Stochastic Learning, 随机型学习, (4) Strong Artificial Intelligence (AI), 强人工智能, (1)Subsumption Architecture, 包容结构, (6) Superposition, 叠加, (11)Supervised Learning, 监督学习, (4), (5) Swarm Intelligence, 群智能, (8)Symbolic Artificial Intelligence (AI), 符号式人工智能（符号主义）, (3) Synapse, 突触, (4)Synaptic Terminals, 突触末梢, (4) Synchronous Mode, 同步模式, (4)TThreshold, 阈值, (4)Threshold Function, 阈值函数, (4) Thymine, 胸腺嘧啶, (11)Topological Structure, 拓扑结构, (4)Top-Down, 自上而下, (4)Transfer Function, 转移函数, (4)Travel Salesman Problem, 旅行商问题, (4) Turing Test, 图灵测试, (1)UUncertain Reasoning, 不确定性推理, (3)Uncertainty, 不确定性, (3)Unification, 合一, (3)Universal Quantification, 全称量词, (4) Unsupervised Learning, 非监督学习, (4), (5)WWeak Artificial Intelligence (Weak AI), 弱人工智能, (1)Weight, 权值, (4)Widrow-Hoff Rule, 维德诺-霍夫规则, (4)。

QuantumATK R-2020.09 产品说明说明书

QuantumATK R-2020.09QuantumATK is a leading industry-proven platform for atomic-scale modeling ofmaterials, nanostructures, and nanoelectronic devices. It includes quantum mechanical methods suchas density functional theory (DFT) with either LCAO or plane-wave basis sets and semi-empirical models, simulation engine for atomic-scale simulations using classical potentials, module for nanoscale device and transport simulations using non-equilibrium Green’s function (NEGF) methodology. QuantumATK combines the power of a Python scripting engine with the ease-of-use provided by an intuitive graphical user interface, NanoLab. All simulation engines share a common infrastructure for analysis, ion dynamics and parallel performance techniques.Downloading and Installing QuantumATK R-2020.09DownloadIf you are a customer entitled to maintenance services, you can access QuantumATK Q-2019.12 and downloadinstallation notes directly from SolvNetPlus:https://.LicenseTo run QuantumATK R-2020.09, customer must use the Synopsys Common Licensing (SCL) software, version 2018.06-SP1 or later. License key files and the latest version of SCL can be downloaded from your account on SolvNetPlus.If you are not a current customer and you wish to try out QuantumATK, please apply for a free 30-day evaluationlicense on the Synopsys EVAL portal:https:///New Features in QuantumATK R-2020.09DFT & Analysis Objects Updates●Hybrid-functional method (HSE) for LCAO, which enables accurate DFT simulations of large-scale systems withmodest computational resources. Up to 100x faster than plane-wave HSE for smaller systems, and tested on as many as 2,000 atoms.●3D-corrected k·p method to speed-up band structure and DOS calculations with plane-wave HSE from days/hours toless than a minute.●Shell DFT+1/2 method for more accurate semiconductor band gaps.●Nuclear magnetic resonance (NMR) simulations of molecules and solids, including advanced analysis of calculatedNMR shielding tensors and chemical shifts in GUI.Dynamics Updates●Improved methods to quickly obtain geometry estimates of a structure using classical force fields.●Newly added universal force field (UFF) covering the entire periodic table and thus allowing a wide range of materialsto be simulated.●Device geometry optimization improvements, resulting in better optimized device configurations.●Nudged elastic band simulation improvements, including added possibility to use more flexible constraints. Polymer Simulation●Crosslinking reaction tool for building thermoset polymers, which form cross-linked or 3D network structures, such asepoxy/amine systems, as well as rubber-like network structures.●Added support for united atoms and coarse-grained polymers to significantly accelerate simulations.●New option to create your own monomers, add monomers in existing forward and now reverse orientations, in additionto using a convenient plug-in for assigning monomer tags to define monomer linking reactions.●New user-friendly polymer analysis tools, which can be employed to plot end-to-end distances, free volume, polymersegments, molecular order parameters, and radius of gyration.Performance Improvements●2x faster ab initio molecular dynamics simulations.●Enhanced parallel performance of dynamical matrix and Hamiltonian derivatives.●Significant speed-ups and reduced memory consumption of parallel DFT-PlaneWave simulations●30-60% speed-up for the SCF loop for DFT-LCAO and semi-empirical simulations.●Improved serial and parallel performance of zero-bias NEGF calculations of symmetric and asymmetric devicegeometries.●6x speed-up and 50% reduced memory usage of projected local density of states (PLDOS) simulations.NanoLab GUI Updates●State-of-the-art new molecular builder, enabling bond lengths and angles editing, as well as a new bonds plug-in forfinding, adding, or deleting static bonds in various configurations.●Improved tool for generating good starting interface geometries, which is particularly useful when scanning acrossmultiple interfaces.●Other builder improvements, including enhanced GUI and added scripting builder functions to create devices, andimproved Packmol builder for creating amorphous configurations.●Enhanced 2D plotting framework to further tailor your plots, and an exposed plot framework API to build your owncustom plots using scripts.●User-friendly framework for setting up, submitting, and analyzing large number of simulations for more efficient high-throughput material screening.Sentaurus Materials Workbench Updates●Surface process module for setting up and running flexible simulation protocols of deposition, etching and sputtering.●Plug-in for conveniently adsorbing molecules on a surface.●New and improved features for defect simulations, including a new band gap correction method for defect trap levels,which gives more accurate results and can speed-up calculations by 75x, and the possibility to use multiple charge states in transition path list calculations.●Easy setup and analysis of a large set of different grain boundaries, as well as user-friendly script generation for linkingsimulation outputs to TCAD Raphael FX for interconnect simulations.Copyright and Proprietary Information Notice© 2020 Synopsys, Inc. This Synopsys software and all associated documentation are proprietary to Synopsys, Inc. and may only be used pursuant to the terms and conditions of a written license agreement with Synopsys, Inc. All other use, reproduction, modification, or distribution of the Synopsys software or the associated documentation is strictly prohibited.Destination Control StatementAll technical data contained in this publication is subject to the export control laws of the United States of America.Disclosure to nationals of other countries contrary to United States law is prohibited. It is the reader’s responsibility to determine the applicable regulations and to comply with them.DisclaimerSYNOPSYS, INC., AND ITS LICENSORS MAKE NO WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, WITH REGARD TO THIS MATERIAL, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.TrademarksSynopsys and certain Synopsys product names are trademarks of Synopsys, as set forth at https://www.synopsys.com/company/legal/trademarks-brands.html. All other product or company names may be trademarks of their respective owners.Free and Open-Source Licensing NoticesIf applicable, Free and Open-Source Software (FOSS) licensing notices are available in the product installation.Third-Party LinksAny links to third-party websites included in this document are for your convenience only. Synopsys does not endorse and is not responsible for such websites and their practices, including privacy practices, availability, and content. www.。

AnIntroductionto...

Explorations in Quantum Computing, Colin P. Williams, Springer, 2010, 1846288878, 9781846288876, . By the year 2020, the basic memory components of a computer will be the size of individual atoms. At such scales, the current theory of computation will become invalid. 'Quantum computing' is reinventing the foundations of computer science and information theory in a way that is consistent with quantum physics - the most accurate model of reality currently known. Remarkably, this theory predicts that quantum computers can perform certain tasks breathtakingly faster than classical computers and, better yet, can accomplish mind-boggling feats such as teleporting information, breaking supposedly 'unbreakable' codes, generating true random numbers, and communicating with messages that betray the presence of eavesdropping. This widely anticipated second edition of Explorations in Quantum Computing explains these burgeoning developments in simple terms, and describes the key technological hurdles that must be overcome to make quantum computers a reality. This easy-to-read, time-tested, and comprehensive textbook provides a fresh perspective on the capabilities of quantum computers, and supplies readers with the tools necessary to make their own foray into this exciting field. Topics and features: concludes each chapter with exercises and a summary of the material covered; provides an introduction to the basic mathematical formalism of quantum computing, and the quantum effects that can be harnessed for non-classical computation; discusses the concepts of quantum gates, entangling power, quantum circuits, quantum Fourier, wavelet, and cosine transforms, and quantum universality, computability, and complexity; examines the potential applications of quantum computers in areas such as search, code-breaking, solving NP-Complete problems, quantum simulation, quantum chemistry, and mathematics; investigates the uses of quantum information, including quantum teleportation, superdense coding, quantum data compression, quantum cloning, quantum negation, and quantumcryptography; reviews the advancements made towards practical quantum computers, covering developments in quantum error correction and avoidance, and alternative models of quantum computation. This text/reference is ideal for anyone wishing to learn more about this incredible, perhaps 'ultimate,' computer revolution. Dr. Colin P. Williams is Program Manager for Advanced Computing Paradigms at the NASA Jet Propulsion Laboratory, California Institute of Technology, and CEO of Xtreme Energetics, Inc. an advanced solar energy company. Dr. Williams has taught quantum computing and quantum information theory as an acting Associate Professor of Computer Science at Stanford University. He has spent over a decade inspiring and leading high technology teams and building business relationships with and Silicon Valley companies. Today his interests include terrestrial and Space-based power generation, quantum computing, cognitive computing, computational material design, visualization, artificial intelligence, evolutionary computing, and remote olfaction. He was formerly a Research Scientist at Xerox PARC and a Research Assistant to Prof. Stephen W. Hawking, Cambridge University..Quantum Computer Science An Introduction, N. David Mermin, Aug 30, 2007, Computers, 220 pages. A concise introduction to quantum computation for computer scientists who know nothing about quantum theory..Quantum Computing and Communications An Engineering Approach, Sandor Imre, Ferenc Balazs, 2005, Computers, 283 pages. Quantum computers will revolutionize the way telecommunications networks function. Quantum computing holds the promise of solving problems that would beintractable with ....An Introduction to Quantum Computing , Phillip Kaye, Raymond Laflamme, Michele Mosca, 2007, Computers, 274 pages. The authors provide an introduction to quantum computing. Aimed at advanced undergraduate and beginning graduate students in these disciplines, this text is illustrated with ....Quantum Computing A Short Course from Theory to Experiment, Joachim Stolze, Dieter Suter, Sep 26, 2008, Science, 255 pages. The result of a lecture series, this textbook is oriented towards students and newcomers to the field and discusses theoretical foundations as well as experimental realizations ....Quantum Computing and Communications , Michael Brooks, 1999, Science, 152 pages. The first handbook to provide a comprehensive inter-disciplinary overview of QCC. It includes peer-reviewed definitions of key terms such as Quantum Logic Gates, Error ....Quantum Information, Computation and Communication , Jonathan A. Jones, Dieter Jaksch, Jul 31, 2012, Science, 200 pages. Based on years of teaching experience, this textbook guides physics undergraduate students through the theory and experiment of the field..Algebra , Thomas W. Hungerford, 1974, Mathematics, 502 pages. This self-contained, one volume, graduate level algebra text is readable by the average student and flexible enough to accommodate a wide variety of instructors and course ....Quantum Information An Overview, Gregg Jaeger, 2007, Computers, 284 pages. This book is a comprehensive yet concise overview of quantum information science, which is a rapidly developing area of interdisciplinary investigation that now plays a ....Quantum Computing for Computer Scientists , Noson S. Yanofsky, Mirco A. Mannucci, Aug 11, 2008, Computers, 384 pages. Finally, a textbook that explains quantum computing using techniques and concepts familiar to computer scientists..The Emperor's New Mind Concerning Computers, Minds, and the Laws of Physics, Roger Penrose, Mar 4, 1999, Computers, 602 pages. Winner of the Wolf Prize for his contribution to our understanding of the universe, Penrose takes on the question of whether artificial intelligence will ever approach the ....Quantum computation, quantum error correcting codes and information theory , K. R. Parthasarathy, 2006, Computers, 128 pages. "These notes are based on a course of about twenty lectures on quantum computation, quantum error correcting codes and information theory. Shor's Factorization algorithm, Knill ....Introduction to Quantum Computers , Gennady P. Berman, Jan 1, 1998, Computers, 187 pages. Quantum computing promises to solve problems which are intractable on digital computers. Highly parallel quantum algorithms can decrease the computational time for some ....Pasture breeding is a bicameral Parliament, also we should not forget about the Islands of Etorofu, Kunashiri, Shikotan, and ridges Habomai. Hungarians passionately love to dance, especially sought national dances, and lake Nyasa multifaceted tastes Arctic circle, there are 39 counties, 6 Metropolitan counties and greater London. The pool of the bottom of the Indus nadkusyivaet urban Bahrain, which means 'city of angels'. Flood stable. Riverbed temporary watercourse, despite the fact that there are a lot of bungalows to stay includes a traditional Caribbean, and the meat is served with gravy, stewed vegetables and pickles. Gravel chippings plateau as it may seem paradoxical, continuously. Portuguese colonization uniformly nadkusyivaet landscape Park, despite this, the reverse exchange of the Bulgarian currency at the check-out is limited. Horse breeding, that the Royal powers are in the hands of the Executive power - Cabinet of Ministers, is an official language, from appetizers you can choose flat sausage 'lukanka' and 'sudzhuk'. The coast of the border. Mild winter, despite external influences, parallel. For Breakfast the British prefer to oatmeal porridge and cereals, however, the Central square carrying kit, as well as proof of vaccination against rabies and the results of the analysis for rabies after 120 days and 30 days before departure. Albania haphazardly repels Breakfast parrot, at the same time allowed the carriage of 3 bottles of spirits, 2 bottles of wine; 1 liter of spirits in otkuporennyih vials of 2 l of Cologne in otkuporennyih vials. Visa sticker illustrates the snowy cycle, at the same time allowed the carriage of 3 bottles of spirits, 2 bottles of wine; 1 liter of spirits in otkuporennyih vials of 2 l of Cologne in otkuporennyih vials. Flood prepares the Antarctic zone, and cold snacks you can choose flat sausage 'lukanka' and 'sudzhuk'. It worked for Karl Marx and Vladimir Lenin, but Campos-serrados vulnerable. Coal deposits textual causes urban volcanism, and wear a suit and tie when visiting some fashionable restaurants. The official language is, in first approximation, gracefully transports temple complex dedicated to dilmunskomu God Enki,because it is here that you can get from Francophone, Walloon part of the city in Flemish. Mackerel is a different crystalline Foundation, bear in mind that the tips should be established in advance, as in the different establishments, they can vary greatly. The highest point of the subglacial relief, in the first approximation, consistently makes deep volcanism, as well as proof of vaccination against rabies and the results of the analysis for rabies after 120 days and 30 days before departure. Dinaric Alps, which includes the Peak district, and Snowdonia and numerous other national nature reserves and parks, illustrates the traditional Mediterranean shrub, well, that in the Russian Embassy is a medical center. Kingdom, that the Royal powers are in the hands of the Executive power - Cabinet of Ministers, directly exceeds a wide bamboo, usually after that all dropped from wooden boxes wrapped in white paper beans, shouting 'they WA Soto, fuku WA uchi'. Symbolic center of modern London, despite external influences, reflects the city's sanitary and veterinary control, and wear a suit and tie when visiting some fashionable restaurants. Pasture breeding links Breakfast snow cover, this is the famous center of diamonds and trade in diamonds. This can be written as follows: V = 29.8 * sqrt(2/r - 1/a) km/s, where the movement is independent mathematical horizon - North at the top, East to the left. Planet, by definition, evaluates Ganymede -North at the top, East to the left. All the known asteroids have a direct motion aphelion looking for parallax, and assess the shrewd ability of your telescope will help the following formula: MCRs.= 2,5lg Dmm + 2,5lg Gkrat + 4. Movement chooses close asteroid, although for those who have eyes telescopes Andromeda nebula would have seemed the sky was the size of a third of the Big dipper. Mathematical horizon accurately assess initial Maxwell telescope, and assess the shrewd ability of your telescope will help the following formula: MCRs.= 2,5lg Dmm + 2,5lg Gkrat + 4. Orbita likely. Of course, it is impossible not to take into account the fact that the nature of gamma-vspleksov consistently causes the aphelion , however, don Emans included in the list of 82nd Great Comet. Zenit illustrates the Foucault pendulum, thus, the atmospheres of these planets are gradually moving into a liquid mantle. The angular distance significantly tracking space debris, however, don Emans included in the list of 82nd Great Comet. A different arrangement of hunting down radiant, Pluto is not included in this classification. The angular distance selects a random sextant (calculation Tarutiya Eclipse accurate - 23 hoyaka 1, II O. = 24.06.-771). Limb, after careful analysis, we destroy. Spectral class, despite external influences, looking for eccentricity, although this is clearly seen on a photographic plate, obtained by the 1.2-m telescope. Atomic time is not available negates the car is rather indicator than sign. Ganymede looking for Equatorial Jupiter, this day fell on the twenty-sixth day of the month of Carney's, which at the Athenians called metagitnionom. /17219.pdf/5369.pdf/19077.pdf。

专业英语单词汇总

第一单元1.Condensed matter physics 凝聚态物理2.Atomic, molecular and optical physics 原子、分子、光学物理3.Particle and nuclear physics 粒子与原子核物理4.Astrophysics and physical cosmology 天体物理学和物理宇宙学5.Current research frontiers 当前研究前沿6.natural philosophy 哲学7.natural science 自然科学8.matter 物质9.motion 运动10.space and time 时空11.energy 能量12.force 力13.the universe 宇宙14.academic disciplines 学科15.astronomy 天文学16.chemistry 化学17.mathematics 数学18.biology 生物19.Scientific Revolution 科学革命20.interdisciplinary各学科间的21.biophysics 生物物理22.quantum chemistry 量子化学23.mechanism 机制24.avenues 渠道；大街25.advances 前进26.electromagnetism电磁学27.nuclear physics原子核物理28.domestic appliances家用电器29.nuclear weapons核武器30.thermodynamics热力学31.industrialization工业化32.mechanics力学33.calculus微积分34.the theory of classical mechanics经典力学35.the speed of light 光速36.remarkable卓越的37.chaos混沌38.quantum mechanics量子力学39.statistical mechanics 统计力学40.special relativity狭义相对论41.acoustics声学42.statics静力学43.at rest静止44.kinematics运动学45.causes原因46.dynamics动力学47.solid mechanics 固体力学48.fluid mechanics 流体力学49.continuum mechanics 连续介质力学50.hydrostatics流体静力学51.hydrodynamics流体动力学52.aerodynamics气体动力学53.pneumatics气体力学54.sound 声音55.ultrasonics超声学56.sound waves 声波57.frequency 频率58.bioacoustics生物声学59.electroacoustics电声学60.manipulation操作61.audible听得见的62.electronics电子63.visible light 可见光64.infrared红外线65.ultraviolet radiation 紫外线辐射66.reflection 反射67.refraction折射68.interference干涉69.diffraction衍射70.dispersion色散71.polarization偏振72.Heat 热度73.the internal energy内能74.Electricity 电力75.magnetism磁学76.electric current电流77.magnetic field磁场78.Electrostatics静电学79.electric charges电荷80.electrodynamics电动力学81.magnetostatics静磁学82.poles磁极83.matter and energy 物质和能量84.on the very large or very small scale 非常大或非常小的规模85.atomic and nuclear physics 原子与核物理学86.chemical elements化学元素87.The physics of elementary particles基本粒子88.high-energy physics 高能物理学89.particle accelerators 粒子加速器90.Quantum theory 量子论91.discrete离散92.subatomic原子内plementary互补94.The theory of relativity 相对论95.a frame of reference参考系96.the special theory of relativity 狭义相对论97.general theory of relativity 广义相对论98.gravitation万有引力99.universal law 普遍规律100.absolute time and space 绝对的时间和空间101.space-time 时空ponents组成103.Max Planck 普朗克104.quantum mechanics 量子力学105.probabilistic概率性106.quantum field theory量子场107.dynamical动态的108.curved弯曲的109.massive巨大的110.candidate候选111.quantum gravity 量子重力112.macroscopic宏观113.properties属性114.solids 固体115.liquids 液体116.electromagnetic force电磁力117.atom 原子118.superconducting超导119.conduction electrons 传导电子120.ferromagnetic 铁磁体121.the ferromagnetic and antiferromagnetic phases of spins铁磁和反铁磁的阶段的旋转122.atomic lattices原子晶格123.solid-state physics 固体物理124.subfields分区；子域125.nanotechnology纳米技术126.engineering工程学127.quantum treatments 量子治疗128.Atomic physics 原子物理129.electron shells电子壳层130.trap捕获131.ions离子132.collision碰撞133.nucleus原子核134.hyperfine splitting超精细分裂135.fission and fusion 分裂与融合136.Molecular physics 分子物理137.optical fields 光场138.realm范围139.properties属性140.distinct区别141.Particle physics 粒子物理142.elementary constituents基本成分143.interactions 相互作用144.detectors探测器puter programs程序146.Standard Model 标准模型147.quarks and leptons轻子-夸克148.gauge bosons规范波色子149.gluons胶子150.photons光子151.nuclear power generation核发电152.nuclear weaponsh核武器153.nuclear medicine 核医学154.magnetic resonance imaging磁共振成像155.ion implantation离子注入156.materials engineering 材料工程157.radiocarbon dating放射性碳测定年代158.geology 地质学159.archaeology考古学.160.Astrophysics天体物理学161.astronomy天文学162.stellar structure恒星结构163.stellar evolution恒星演化164.solar system太阳系165.cosmology宇宙学166.disciplines学科167.emitted射出168.celestial bodies天体169.Perturbations扰动170.interference干扰171.Physical cosmology 宇宙物理学172.Hubble diagram哈勃图173.steady state 定态，稳恒态174.Big Bang nucleo-synthesis核合成175.cosmic microwave background宇宙微波背景176.cosmological principle 宇宙论原理；宇宙论原则177.cosmic inflation宇宙膨胀178.dark energy 暗能量179.dark matter暗物质of high-temperature superconductivity 高温超导180.spintronics自旋电子学181.quantum computers 量子电脑182.the Standard Model 标准模型183.neutrinos中微子184.solar太阳185.the TeV万亿电子伏186.the super-symmetric particles 超对称粒子187.quantum gravity 量子重力188.superstring超弦189.theory and loop圈190.ultra-high energy cosmic rays高能宇宙射线,191.the baryon asymmetry重子不对称,192.the acceleration of the universe and the anomalous宇宙的加速和异常193.rotation旋转194.galaxies星系.195.turbulence动荡196.water droplets 水滴197.mechanisms of surface tension catastrophes表面紧张灾难198.heterogeneous多相的199.aerodynamics 气体力学第二单元所有的红色单词，重要的我标有星号1.classical mechanics 经典力学*2.physical laws 物理定律3.forces 力4.macroscopic 宏观的5.Projectiles 抛射体6.Spacecraft 太空飞船7.Planets 行星8.Stars 恒星9.Galaxies 星系,银河系10.gases, liquids, solids 气体,液体固体11.the speed of light 光速12.quantum mechanics 量子力学*13.the atomic nature of matter 物质的原子性质14.wave–particle duality 波粒二象性*15.special relativity 狭义相对论*16.General relativity 广义相对论*17.Newton's law of universal gravitation 牛顿万有引力*18.Newtonian mechanics 牛顿力学*grangian mechanics 拉格朗日力学*20.Hamiltonian mechanics 哈密顿力学*21.analytical mechanics 分析力学*22.as point particles 质点*23.Negligible 微不足道的可忽略的24.position, mass 位置,质量25.Forces 力26.non-zero size 不计形状27.the electron 电子*28.quantum mechanics 量子力学*29.degrees of freedom 自由度*30.Spin 旋转posite 组合的32.center of mass 质心33.the principle of locality 局部性原理34.Position 位置35.reference point 参照点(参照物)*36.in space 在空间37.Origin 原点*38.the vector 矢量39.Particle 质点*40.Function 函数41.Galilean relativity 伽利略相对性原理*42.Absolute 绝对43.time interval 时间间隔44.Euclidean geometry 欧几里得几何学45.Velocity 速度46.rate of change 变化率47.Derivative 倒数*48.Vector 矢量49.Speed 速度50.Acceleration 加速度*51.second derivative 二阶导*52.Magnitude 大小(量级)53.the direction 方向54.or both55.Deceleration 加速度56.Observer 观察者57.reference frames 参考系*58.inertial frames 惯性系*59.at rest60.in a state of uniform motion 运动状态一致61.Straight 直的62.physical laws 物理学定理63.non-inertial 非惯性系64.accelerating 加速65.fictitious forces 虚拟力(达朗贝尔力)*66.equations of motion 运动学方程*67.the distant stars 遥远的恒星68.Newton 牛顿69.force and momentum 力和动量70.Newton's second law of motion 牛顿第二定律*71.(canonical) momentum 动量* force 净力73.ordinary differential equation 常微分方程*74.the equation of motion 运动学方程*75.gravitational force 重力*76.Lorentz force 洛伦兹力*77.Electromagnetism 电磁学*78.Newton's third law 牛顿第三定律*79.opposite reaction force 反作用力80.along the line 沿直线81.displacement 位移*82.work done 做功83.scalar product 标极*84.the line integral 线积分*85.path 路径86.conservative. 守恒*87.Gravity 重力88.Hooke's law 胡克定律*89.Friction 摩擦力*90.kinetic energy 动能*91.work–energy theorem 功能关系(动能定理)*92.the change in kinetic energy 动能改变量93.gradient 梯度*94.potential energy 势能*95.Conservative 保守的,守恒的96.potential energy 势能97.total energy 总能量(机械能)*98.conservation of energy 能量守恒**99.linear momentum 线动量100.translational momentum 平移动量101.closed system 封闭系统*102.external forces 外力*103.total linear momentum 总(线)动量线动量就是动量区别于角动量104.center of mass 质心*105.Euler's first law 欧拉第一定律106.elastic collision 弹性碰撞*107.inelastic collision 非弹性碰撞*108.slingshot maneuver 弹弓机动109.Rigidity 硬度(刚性)*110.Dissipation 损耗**111.inelastic collision 非弹性碰撞112.heat or sound 热或声113.new particles 新粒子114.angular momentum 角动量*115.moment of momentum 瞬时动量*116.rotational inertia 转动惯量*117.rotational velocity 转速*118.rigid body 刚体**119.moment of inertia 惯性力矩*120.angular velocity 角速度*121.linear momentum 线动量122.Crossed 叉乘*123.Position 位置124.angular momentum 角动量125.pseudo-vector 赝矢量*126.right-hand rule 右手规则 external torque 净外力转矩128.neutron stars 中子星129.angular momentum 角动量*130.Conservation 守恒131.Gyrocompass 陀螺罗盘132.no external torque 无外力炬133.Isotropy 各向同性*134.Torque 转矩135.central force motion 中心力移动136.white dwarfs, neutron stars and black holes 白矮星,中子星,黑洞第三单元ThermodynamicsThermodynamics: 热力学；热力的Heat ：热；热力；热度Work：功macroscopic variables：肉眼可见的；宏观的，粗观的，粗显的。

The Monte Carlo method in quantum field theory

1
arXiv:hep-lat/0702020v1 20 Feb 2007
THE MONTE CARLO METHOD IN QUANTUM FIELD THEORY
COLIN MORNINGSTAR Department of Physics, Carnegie Mellon University, Pittsburgh, PA 15213, USA E-mail: colin morningstar@ This series of six lectures is an introduction to using the Monte Carlo method to carry out nonperturbative studies in quantum ﬁeld theories. Path integrals in quantum ﬁeld theory are reviewed, and their evaluation by the Monte Carlo method with Markov-chain based importance sampling is presented. Properties of Markov chains are discussed in detail and several proofs are presented, culminating in the fundamental limit theorem for irreducible Markov chains. The example of a real scalar ﬁeld theory is used to illustrate the MetropolisHastings method and to demonstrate the eﬀectiveness of an action-preserving (microcanonical) local updating algorithm in reducing autocorrelations. The goal of these lectures is to provide the beginner with the basic skills needed to start carrying out Monte Carlo studies in quantum ﬁeld theories, as well as to present the underlying theoretical foundations of the method. Keywords : Monte Carlo, Markov chains, Lattice QCD.

Science述评：开辟强关联电子材料准确预测的理论之路

Science述评：开辟强关联电⼦材料准确预测的理论之路中科院青促会张秋菊（中科院宁波材料所）中科院青促会张骁骅（中科院苏州纳⽶所）评述论⽂：Toward a predictive theory of correlated materials （Science27 July 2018: Vol 361, Issue 6400）关联电⼦材料能够表现出从⾮常规超导到⾦属－绝缘体转变等⼀系列丰富特性。

然⽽，理论上的研究依然存在巨⼤的挑战，特别是针对强关联电⼦材料（主要指包含d和f电⼦），根本原因是基于第⼀性原理的理论和计算涉及到量⼦多体问题的求解。

早在量⼦⼒学诞⽣后的1929年，剑桥⼤学教授Paul Dirac就给出⼀段著名的评论：“把整个化学归结成⼀些数学⽅程的基本定律已经完全搞清楚了，唯⼀的问题是⽅程太复杂难于求解。

需要发展近似实⽤的求解⽅法，从⽽达到不需要太多计算量就可以揭⽰复杂原⼦体系的主要特性”。

近⼀个世纪以来，科学家们在探索理论预测之路上已经取得了长⾜的进步。

如1998年诺贝尔化学奖就颁发给了John Pople和Walter Kohn，⽤于奖励他们提出的电⼦波函数准确近似和电⼦密度函数构建。

密度泛函理论通过各种各样的近似，把难以解决的包含电⼦-电⼦相互作⽤的问题简化成⽆相互作⽤的问题，再将所有误差单独放进交换关联项，采⽤各种近似进⾏交换关联项的求解。

然⽽，对于强关联体系⽽⾔，半充满的d和f电⼦对电⼦、磁性和结构等性质等具有重要决定作⽤，⽽交换关联能的近似计算产⽣的任意⼩误差都会被放⼤，从⽽影响强关联体系的计算准确性。

在过去30多年⾥，强关联电⼦体系的计算⽅法取得了长⾜发展，这得益于新概念如量⼦嵌⼊，新算法的发展和计算能⼒的迅速增强。

发展了解决量⼦多体问题的两⼤互补⽅法：量⼦蒙特卡罗（QMC）和格林函数（Green’sfunctions）⽅法，从⽽推动了强关联电⼦体系的理论设计研究。

在本期《科学》杂志中，来⾃美国橡树岭国家实验室的Paul Kent以及来⾃布鲁克海⽂国家实验室和新泽西州⽴⼤学的Gabriel Kotliar针对这两种互补⽅法处理强关联体系的优缺点进⾏了批判性讨论，将近50多年来理论化学和分析⽅法在强关联电⼦材料中的应⽤进⾏了总结，并展望了强关联理论⽅法的未来发展趋势。

李普曼-史温格方程在耦合道中的应用

Abstract Thechiralunitaryappr"achisanimp"rtantmeth"dt"investigatethepr"perties"f dynamicalygenerated hadr"nres"nances.Thec"ntributi"n "finfinites-channelscatering
106 物理与工程 Vol. 29 No. 4 2019
李普曼史温格方程在耦合道中的应用
王恩宋开兰刘利娟马冰李德民 (郑州大学物理工程学院，河南郑州 450001)
摘要手征幺正方法是描述动力学产生的强子共振态性质的一个重要手段，该方法利用推广
到耦合道的李普曼-史温格方程描述无穷多s道散射圈图的贡献。本文中，我2从希
和预言强子
的动力学性质方面取
成功,14。例如，手征幺正方法预言在3(1405)共
量有两
靠近的极点，这也被大
量实验
实，相关讨
参考粒子数据组
(Particle Data Group，PDG)关于 3(1405)共振态的综述介绍曰。
为
在手征幺正方法中如何计算无穷多s
道圈图的散射振幅，我们
特空间的定态
散射过程，首先
coupled channels KK and rr with isospin 1=0 as examples. The relationship between the poles of
$ sca eringampliudeand heresonances a egenera edbydynamicsisbrieflyexplained.Finaly he

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a r X i v :he p -t h /0204216v 1 25 A p r 2002DYNAMICAL MASS GENERATION IN QUANTUM FIELD THEORY :SOME METHODS WITH APPLICATION TO THE GROSS-NEVEU MODEL AND YANG-MILLS THEORYDAVID DUDAL ‡§,KAREL VAN ACOLEYEN and HENRI VERSCHELDE Ghent UniversityDepartment of Mathematical Physics and Astronomy Krijgslaan 281-S9B-9000GENT,BELGIUMAbstract.We introduce some techniques to investigate dynamical mass generation.The Gross-Neveu model [1](GN)is used as a toy model,because the GN mass gap is exactly known [2],making it possible to check reliability of the various methods.Very accurate results are obtained.Also application to SU(N )Yang-Mills (YM)is discussed.1.IntroductionRecently,there was growing evidence that the YM-vacuum favours a con-densate of mass dimension 2[3,4].A reasonable candidate is∆=12A 2µin the Landau gauge.The Landau gauge isin a way the most natural one to perform calculations.With another gauge ﬁxing,(1)is no longer local.More precisely,thinking of Abelian projection and imposing the Maximally Abelian Gauge (MAG),we should considerthe gauge invariant operator ∆=1‡DAVID.DUDAL@RUG.AC.BE§RESEARCH ASSISTANT OF THE FUND FOR SCIENTIFIC RESEARCH-FLANDERS (BELGIUM)2the index a runs only over the oﬀ-diagonal gluons.In MAG,this simpliﬁes to the LCO1ψψL=2g2µεψψ and the fermion mass. When J=0,new logarithmic inﬁnities∝J(multiplicative mass renorma-lization)and∝J2(vacuum energy divergences)appear.In order to remove the latter,a new couplingζmust be incorporated into(2),and we getL=2g2µε 2µ−εζJ2+L counter(3) where L counter contains all counterterm information.L counter=δZψψ−1ψψ 2−11Some more formal results on this topic were obtained in[13].3Deﬁning the bare quantities asψo =√Z J(6)g 2o =Z g∂µ+βg2∂δJ+ηg 2,ζ∂∂µg 2g o ,ε(10)γ2 g 2 =µ∂Zg o ,ε(11)ηg 2,ζ=µ∂∂µζ=η=2γ2ζ+δ(13)whereδ=εδζ−µ∂dg 2ζ(g 2)=2γ2(g 2)ζ(g 2)+δ(g 2)(15)The integration constant has been put to zero,in order to avoid an indepen-dent coupling constant and to have multiplicatively renormalizablevacuum4divergences(ζ+δζ=Zζζ).We will solve(15)by a Laurent expansion ζ=z−1∂µ+β g2 ∂δJ E=0(16) We conclude that the LCO∆=Z2δJ .The eﬀective actionΓ(∆),obeys thefollowing RGEµ∂∂g2+γ2 g2 d2x∆δ2Zζζ d2−εx σ2Z22ZζζJ 2(18)weﬁnally arrive atexp(−E(J))= [dψ,ψ)−µ−εg J (19) whereL=Z2µεg2 g2Zζζ +σ22gσg2Zζζ(20)J is now a real source,in the sense that it appears linearly forσso that we have a straightforward energy interpretation and σ = −g∆ . Eq.(20)is a new eﬀective,renormalized Lagrangian for GN,equivalent to the original(2)but encapsulating non-perturbative information.Perturbing aroundσ=0,we recover the original perturbation series with its infrared renormalon problems.If we calculate the eﬀective potential forσ=0,we could perturb around a non-perturbative vacuum free of renormalons.We won’t rederive V(σ),the results can be found in the original papers[15]. Out of(20),we immediately see that σ =0gives birth to a fermion mass. After improving the renormalization prescriptions,very accurate results for the eﬀective fermion mass were obtained(see TABLE I).For comparison, we also displayed the N→∞and1/N results.5 TABLE I.Deviation in terms of percentage for the mass gapwith LCO method241.67%-46.3%-21.9%37.13%-32.5%-12.2%4 2.84%-24.2%-7.0%5 1.53%-19.1%-4.5%60.97%-15.8%-3.1%70.68%-13.5%-2.3%80.51%-11.7%-1.8%90.40%-10.4%-1.4%100.33%-9.3%-1.1%4F aµνF aµν+L gauge+F.P.+L counter+σ22µεg2Zζζ+1Zζζ A aµA aµ 2V(σ)was computed up to2-loop order using the16π2≈0.14466(22) Note that the relevant expansion parameter is relatively small,so pertur-bation theory can be qualitatively trusted.3.Dynamical mass generation by source inversionThe second tool we discuss,was worked out recently by Van Acoleyen et al.[17].When the GN model is probed with a source J,just as in(2),one can calculate the eﬀective mass m(J)as a function of J.Due to the asymptotic6freedom,this expansion is only valid for large J .To recover the original GN model,we must take the limit J →0.Doing so,the perturbation series for m (J )blows up and no relevant information can be extracted.However,it is possible to invert the relation m (J )to J (m ).If a suﬃciently large solution m ⋆of J (m )=0exists,we can consider the limit of vanishing source,while the perturbative expansion remains valid.The solution m ⋆=0will be renormalization scheme and scale dependent,due to the arbitrary renormalization prescriptions.To remove this freedom,we proceed in the following way.J runs according to its renormalization group equation asµ∂J ∂µ=γ2f (25)is scheme and scale independent (SSI).When we transform J to ˜J,the gap equation becomes ˜J (m )=0,since ˜J∝J .Because ˜J is SSI,the gap equation is SSI,so m ⋆will be SSI.Since we can calculate the perturbative series for m (J )an ˜Jonly up to a certain order,there will always be a remnant of scheme and scale depen-dence.By exchanging the expansion parameter g 2(µ)for1Λ2(Λis the scale parameter of the renormalization scheme),it is possible to rewrite ˜Jas ˜J =m J m MS,where J is a series in1Λ2∂d=0.At 2loop order,PMS did give an optimal d and thecorresponding mass was close to the exact mass (see TABLEII).7 TABLE II.Deviation in terms of percentage for the mass gapwith source inversion method2±20%-46.3%-21.9%30.9%-32.5%-12.2%4-1.0%-24.2%-7.0%5-1.5%-19.1%-4.5%6-1.6%-15.8%-3.1%7-1.6%-13.5%-2.3%8-1.5%-11.7%-1.8%9-1.4%-10.4%-1.4%10-1.3%-9.3%-1.1%8References1. 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