Continuous time quantum walks in phase space

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Quantum walks on the hypercube

Quantum Walks on the HypercubeC RISTOPHER M OOREComputer Science DepartmentUniversity of New Mexico,Albuquerque and the Santa Fe Institute,Santa Fe,New Mexicomoore@A LEXANDER R USSELL Department of Computer Science and Engineering University of ConnecticutStorrs,Connecticutacr@November12,2001AbstractRecently,it has been shown that one-dimensional quantum walks can mix more quickly than clas-sical random walks,suggesting that quantum Monte Carlo algorithms can outperform their classicalcounterparts.We study two quantum walks on the n-dimensional hypercube,one in discrete time andone in continuous time.In both cases we show that the instantaneous mixing time isπ4n steps,fasterthan theΘn log n steps required by the classical walk.In the continuous-time case,the probabilitydistribution is exactly uniform at this time.On the other hand,we show that the average mixing timeas deﬁned by Aharonov et al.[AAKV01]isΩn32in the discrete-time case,slower than the classical walk,and nonexistent in the continuous-time case.This suggests that the instantaneous mixing time is amore relevant notion than the average mixing time for quantum walks on large,well-connected graphs.Our analysis treats interference between terms of different phase more carefully than is necessary for thewalk on the cycle;previous general bounds predict an exponential average mixing time when applied tothe hypercube.1IntroductionRandom walks form one of the cornerstones of theoretical computer science.As algorithmic tools,theyhave been applied to a variety of central problems,such as estimating the volume of a convex body[DFK91,LK99],approximating the permanent[JS89,JSV00],andﬁnding satisfying assignments for Boolean for-mulae[Sch99].Furthermore,the basic technical phenomena appearing in the study of random walks(e.g.,spectral decomposition,couplings,and Fourier analysis)also support several other important areas such aspseudorandomness and derandomization(see,e.g.,[AS92,(9,15)]).The development of efﬁcient quantum algorithms for problems believed to be intractable for classicalrandomized computation,like integer factoring and discrete logarithm[Sho97],has prompted the investi-gation of quantum walks.This is a natural generalization of the traditional notion discussed above where,roughly,the process evolves in a unitary rather than stochastic fashion.The notion of“mixing time,”theﬁrst time when the distribution induced by a random walk is sufﬁcientlyclose to the stationary distribution,plays a central role in the theory of classical random walks.For a givengraph,then,it is natural to ask if a quantum walk can mix more quickly than its classical counterpart.(Sincea unitary process cannot be mixing,we deﬁne a stochastic process from a quantum one by performinga measurement at a given time or a distribution of times.)Several recent articles[AAKV01,ABN01,NV00]have answered this question in the afﬁrmative,showing,for example,that a quantum walk on then-cycle mixes in time O n log n,a substantial improvement over the classical random walk which requires Θn2steps to mix.Quantum walks were also deﬁned in[Wat01],and used to show that undirected graph connectivity is contained in a version of quantum LOGSPACE.These articles raise the exciting possibilitythat quantum Monte Carlo algorithms could form a new family of quantum algorithms that work morequickly than their classical counterparts.Two types of quantum walks exist in the literature.Theﬁrst,introduced by[AAKV01,ABN01,NV00],studies the behavior of a“directed particle”on the graph;we refer to these as discrete-time quantumwalks.The second,introduced in[FG98,CFG01],deﬁnes the dynamics by treating the adjacency matrixof the graph as a Hamiltonian;we refer to these as continuous-time quantum walks.The landscape isfurther complicated by the existence of two distinct notions of mixing time.The“instantaneous”notion[ABN01,NV00]focuses on particular times at which measurement induces a desired distribution,whilethe“average”notion[AAKV01],another natural way to convert a quantum process into a stochastic one,focuses on measurement times selected randomly from some interval.In this article,we analyze both the continuous-time and a discrete-time quantum walk on the hypercube.In both cases,the walk is shown to have an instantaneous mixing time atπ4n.(Of course,in the discretewalk all times are integers.)Recall that the classical walk on the hypercube mixes in timeΘn log n,sothat the quantum walk is faster by a logarithmic factor.Moreover,in the discrete-time case the walk mixesin time less than the diameter of the graph,sinceπ41;astonishingly,in the continuous-time case theprobability distribution at tπ4n is exactly uniform.Both of these things happen due to a marvelousconspiracy of destructive interference between terms of different phase.These walks show i.)a similarity between the two notions of quantum walks,and ii.)a disparity between the two notions of quantum mixing times.As mentioned above,both walks have an instantaneous mixing time at timeπ4n.On the other hand,we show that the average mixing time of the discrete-time walk isΩn32,slower than the classical walk,and that for the continuous-time walk there is no time at which the time-averaged probability distribution is close to uniform in the sense of[AAKV01].Our results suggest that for large graphs(large compared to their mixing time)the instantaneous notion of mixing time is more appropriate than the average one,since the probability distribution is close to uniform only in a narrow window of time.The analysis of the hypercubic quantum walk exhibits a number of features markedly different fromthose appearing in previously studied walks.In particular,the dimension of the relevant Hilbert space is,for the hypercube,exponential in the length of the desired walk,while in the cycle these quantities are roughly equal.This requires that interference be handled in a more delicate way than is required for the walk on the cycle;in particular,the general bound of[AAKV01]yields an exponential upper bound on the mixing time for the discrete-time walk.We begin by deﬁning quantum walks and discussing various notions of mixing time.We then analyze the two quantum walks on the hypercube in Sections2and3.(Most of the technical details for the discrete-time walk are relegated to an appendix.)1.1Quantum walks and mixing timesAny graph G V E gives rise to a familiar Markov chain by assigning probability1d to all edges leaving each vertex v of degree d.Let P t u v be the probability of visiting a vertex v at step t of the random walk on G starting at u.If G is undirected,connected,and not bipartite,then lim t∞P t u exists1and is independent of u.A variety of well-developed techniques exist for establishing bounds on the rate at which P t u achieves this limit(e.g.,[Vaz92]);if G happens to be the Cayley graph of a group(as are,for example,the cycle and the hypercube),then techniques from Fourier analysis can be applied[Dia88].Below we will use some aspects of this approach,especially the Diaconis-Shahshahani bound on the total variation distance[DS81].For simplicity,we restrict our discussion to quantum walks on Cayley graphs;more general treatments of quantum walks appear in[AAKV01,FG98].Before describing the quantum walk models we set down some notation.For a group G and a set of generatorsΓsuch thatΓΓ1,let X GΓdenote the undirected Cayley graph of G with respect toΓ.For a ﬁnite set S,we let L S f:S denote the collection of-valued functions on S with∑s S f s2 1. This is a Hilbert space under the natural inner product f g∑s S f s g s.For a Hilbert space V,a linear operator U:V V is unitary if for all v w V,v w U v U w;if U is represented as a matrix,this is equivalent to the condition that U†U1where†denotes the Hermitian conjugate.There are two natural quantum walks that one can deﬁne for such graphs,which we now describe.T HE DISCRETE-TIME WALK:This model,introduced by[AAKV01,ABN01,NV00],augments the graph with a direction space,each basis vector of which corresponds one of the generators inΓ.A step of the walk then consists of the composition of two unitary transformations;a shift operator which leaves the direction unchanged while moving the particle in its current direction,and a local transformation which op-erates on the direction while leaving the position unchanged.To be precise,the quantum walk on X GΓis deﬁned on the space L GΓL G LΓ.LetδγγΓbe the natural basis for LΓ,andδg g G the natural basis for L G.Then the shift operator is S:δgδγδgγδγ,and the local transformation isˇD1D where D is deﬁned on LΓalone and1is the identity on L G.Then one“step”of the walk corresponds to the operator UˇDV.If we measure the position of the particle,but not its direction,at time t,we observe a vertex v with probability P t v∑γΓU tψ0δvδγ2whereψ0L GΓis the initial state.T HE CONTINUOUS-TIME WALK:This model,introduced in[FG98],works directly on L G.The walk evolves by treating the adjacency matrix of the graph as a Hamiltonian and using the Schr¨o dinger equation. Speciﬁcally,if H is the adjacency matrix of X GΓ,the evolution of the system at time t is given by U t, where U t eq e iHt(here we use the matrix exponential,and U t is unitary since H is real and symmetric). Then if we measure the position of the particle at time t,we observe a vertex v with probability P t vU tψ0δv2whereψ0is the initial state.Note the analogy to classical Poisson processes:since U t e iHt 1In fact,this limit exists under more general circumstances;see e.g.[MR95].1iHt iHt22,the amplitude of making s steps is the coefﬁcient it s s!of H s,which up to normalization is Poisson-distributed with mean t.Remark.In[CFG01],the authors point out that deﬁning quantum walks in continuous time allows unitarity without having to extend the graph with a direction space and a chosen local operation.On the other hand,it is harder to see how to carry out such a walk in a generically programmable way using only local information about the graph,for instance in a model where we query a graph toﬁnd out who our neighbors are.Instead,continuous-time walks might correspond to special-purpose analog computers,where we build in interactions corresponding to the desired Hamiltonian and allow the system to evolve in continuous time.In both cases we start with an initial wave function concentrated at a single vertex corresponding to the identity u of the group.For the continuous-time walk,this corresponds to a wave functionψ0v ψ0δv(so thatψ0u1andψ0v0for all v u).For the discrete-time walk,we start with a uniform superposition over all possible directions,ψ0vγψ0δvδγ1Γif v u 0otherwise.For the hypercube,u000.In order to deﬁne a discrete-time quantum walk,one must select a local operator D on the directionspace.In principle,this introduces some arbitrariness into the deﬁnition.However,if we wish D to respectthe permutation symmetry of the n-cube,and if we wish to maximize the operator distance between D andthe identity,we show in Appendix A that we are forced to choose Grover’s diffusion operator[Gro96],which we recall below.We call the resulting walk the“symmetric discrete-time quantum walk”on then-cube.(Watrous[Wat01]also used Grover’s operator to deﬁne quantum walks on undirected graphs.)Since for large n Grover’s operator is close to the identity matrix,one might imagine that it would takeΩn12steps to even change direction,giving the quantum walk a mixing time of n32,slower than the classical random walk.However,like many intuitions about quantum mechanics,this is simply wrong.Since the evolution of the quantum walk is governed by a unitary operator rather than a stochastic one,unless P t is constant for all t,there can be no“stationary distribution”lim t∞P t.In particular,for anyε0,there are inﬁnitely many(positive,integer)times t for which U t1εso that U tψuψuεand P t is close to the initial distribution.However,there may be particular stopping times t which induce distributions close to,say,the uniform distribution,and we call these instantaneous mixing times:Deﬁnition1We say that t is anε-instantaneous mixing time for a quantum walk if P t Uε,where A B12∑v A v B v denotes total variation distance and U denotes the uniform distribution.For these walks we show:Theorem1For the symmetric discrete-time quantum walk on the n-cube,t kπ4n is anε-instantaneousmixing time withεO n76for all odd k.and,even more surprisingly,Theorem2For the continuous-time quantum walk on the n-cube,t kπ4n is a0-instantaneous mixingtime for all odd k.Thus in both cases the mixing time isΘn,as opposed toΘn log n as it is in the classical case.Aharonov et al.[AAKV01]deﬁne another natural notion of mixing time for quantum walks,in whichthe stopping time t is selected uniformly from the set0T1.They show that the time-averageddistributions¯P T1T∑T1t0P t do converge as T∞and study the rate at which this occurs.For a continuous-time random walk,we analogously deﬁne the distribution¯P T v1T T0P t v d t.Then we call a time at which¯P T is close to uniform an average mixing time:Deﬁnition2We say that T is anε-average mixing time for a quantum walk if¯P T Uε.In this paper we also calculate theε-average mixing times for the hypercube.For the discrete-time walk,it is even longer than the mixing time of the classical random walk:Theorem3For the discrete-time quantum walk on the n-cube,theε-average mixing time isΩn32ε. This is surprising given that the instantaneous mixing time is only linear in n.However,the probability distribution is close to uniform only in narrow windows around the odd multiples ofπ4n,so¯P T is far from uniform for signiﬁcantly longer times.We also observe that the general bound given in[AAKV01]yields an exponential upper bound on the average mixing time,showing that it is necessary to handle interference for walks on the hypercube more carefully than for those on the cycle.For the continuous-time walk the situation is even worse:while it possesses0-instantaneous mixing times at all odd multiples ofπ4n,the limiting distribution lim T∞¯P T is not uniform,and we show the following:Theorem4For the continuous-time quantum walk on the n-cube,there existsε0such that no time is an ε-average mixing time.Our results suggest that in both the discrete and continuous-time case,the instantaneous mixing time is a more relevant notion than the average mixing time for large,well-connected graphs.2The symmetric discrete-time walkIn this section we prove Theorem1.We treat the n-cube as the Cayley graph of n2with the regular basis vectors e i010with the1appearing in the i th place.Then the discrete-time walk takes place in the Hilbert space L n2n where n1n.Here theﬁrst component represents the position x of the particle in the hypercube,and the second component represents the particle’s current“direction”;if this is i,the shift operator willﬂip the i th bit of x.As in[AAKV01,NV00],we will not impose a group structure on the direction space,and will Fourier transform only over the position space.For this reason,we will express the wave functionψL n2n as a functionΨ:n2n,where the i th coordinate ofΨx is the projection ofψintoδxδi,i.e.the complex amplitude of the particle being at position x with direction i.The Fourier transform of such an elementΨis˜Ψ:n2n,where˜Ψk∑x1k xΨx.Then the shift operator for the hypercube is S:Ψx∑n i1πiΨx e i where e i is the i th basis vector in the n-cube,andπi is the projection operator for the i th direction.The reason for considering the Fourier transform above is that the shift operator isdiagonal in the Fourier basis:speciﬁcally it maps˜Ψk Sk˜Ψk whereS k 1k101k2...01k nFor the local transformation,we use Grover’s diffusion operator on n states,D i j2nδi j.The advantage of Grover’s operator is that,like the n-cube itself,it is permutation symmetric.We use thissymmetry to rearrange UkSkD to put the negated rows on the bottom,UkSkD2n12n2n2n12n......2n12n2n2n2n1......where the top and bottom blocks have n k and k rows respectively;here k is the Hamming weight of k.The eigenvalues of Uk then depend only on k.Speciﬁcally,Ukhas the eigenvalues1and1withmultiplicity k1and n k1respectively,plus the eigenvaluesλλwhereλ12kn2ink n k e iωkandωk0πis described bycosωk12knsinωk2nk n kIts eigenvectors with eigenvalue1span the k1-dimensional subspace consisting of vectors with support on the k“ﬂipped”directions that sum to zero,and similarly the eigenvectors with eigenvalue1span the n k1-dimensional subspace of vectors on the n k other directions that sum to zero.We call these the trivial eigenvectors.The eigenvectors ofλλe iωk arev k v k1in k 1 kWe call these the non-trivial eigenvectors for a given k.Over the space of positions and directions these eigenvectors are multiplied by the Fourier coefﬁcient1k x,so as a function of x and direction1j n the two non-trivial eigenstates of the entire system,for a given k,arev k x j1k x2n21if kj1i n k if k j0with eigenvalue e iωk,and its conjugate vkwith eigenvalue e iωk.We take for our initial wave function a particle at the origin000in an equal superposition of directions.Since its position is aδ-function in real space it is uniform in Fourier space as well as over thedirection space,giving˜Ψ0k2n2n 11This is perpendicular to all the trivial eigenvectors,so theiramplitudes are all zero.The amplitude of its component along the non-trivial eigenvector vkisa k Ψ0vk2n2kni1kn(1)and the amplitude of vk is ak.Note that ak22n2,so a particle is equally likely to appear in eithernon-trivial eigenstate with any given wave vector.At this point,we note that there are an exponential number of eigenvectors in which the initial state has a non-zero amplitude.In Section2.1,we observe that for this reason the general bound of Aharonov et al. [AAKV01]yields an exponential(upper)bound on the mixing time.In general,this bound performs poorly whenever the number of important eigenvalues is greater than the mixing time.Instead,we will use the Diaconis-Shahshahani bound on the total variation distance in terms of the Fourier coefﬁcients of the probability[Dia88].If P t x is the probability of the particle being observed at position x at time t,and U is the uniform distribution,then the total variation distance is bounded byP t U214∑k00k11˜Pt k214n1∑k1nk˜Pt k2(2)Here we exclude both the constant term and the parity term k 11;since our walk changes position at every step,we only visit vertices with odd or even parity at odd or even times respectively.Thus U here means the uniform distribution with probability 2n 1on the vertices of appropriate parity.To ﬁnd ˜Pt k ,we ﬁrst need ˜Ψt k .As Nayak and Vishwanath [NV00]did for the walk on the line,we start by calculating the t th matrix power of U k .This isU t k a 1t aa a1t c ......b 1t bc bb 1t ......wherea cos ωk t 1t n k b cos ωk t 1t k and c sin ωk t Starting with the uniform initial state,the wave function after t steps is˜Ψt k 2n 2n cos ωk t n k sin ωk t n kcos ωk t n kksin ωk t k (3)In the next two sections we will use this diagonalization to calculate the average and instantaneous mixing times,which are Ωn 32and Θn respectively.2.1Bounds on the average mixing time of the discrete-time walkIn this section,we prove Theorem 3.To do this,it’s sufﬁcient to calculate the amplitude at the origin.Fouriertransforming Equation 3back to real space at x 00gives ψt 02n 2∑k ˜Ψt k 2n n n ∑k 0n k cos ωk t cos ωk tnThe probability the particle is observed at the origin after t steps is thenP t 0ψt 022nn ∑k 0n k cos ωk t 2Let k 1x n 2.For small x ,k is near the peak of the binomial distribution,and ωk cos 1x π2x O x 3so the angle θbetween ωk for successive values of k is roughly constant,θ2n O x 2leading to constructive interference if θt 2π.Speciﬁcally,let t m be the even integer closest to πmn forinteger m .Then cos ωk t mcos 2πkm O x 3mn 1O x 6m 2n 2.By a standard Chernoff bound,2n ∑k 1x n 2n k o 1so long as x ωn 12.Let x νn n 12where νn is a function that goes to inﬁnity slowly as a function of n .We then write P t 0o 12n1x n 2∑k 1x n 2n k 1O x 6m 2n 221O νn 6m 2nwhich is 1o 1as long as m o n 12νn 3,in which case t mo n 32νn 3.For a functionψ:n2n withψ21and a set S n2,we say thatψis c-supported on S if the probability x S is at least c,i.e.∑x S d nψx d2c.The discussion above shows thatψt m is 1o1-supported on0for appropriate t mπmn.Note that ifψis c-supported on0then,as U is local,U kψmust be c1c2c1-supported on W k,the set of vertices of weight k.(The factor of1c is due to potential cancellation with portions of the wave function supported outside0.)Inparticular,at times t m k,for k n2n,ψt m k is1o1-supported on W n2x.If x x nωn,then W12δn2n o1and,evidently,the average1T∑T i P i has total variation distance1o1from the uniform distribution if T o n32.Thus we see that in the sense of[AAKV01],the discrete-time quantum walk is actually slower than the classical walk.In the next section,however,we show that its instantaneous mixing time is only linear in n.We now observe that the general bound of[AAKV01]predicts an average mixing time for the n-cube which is exponential in n.In that article it is shown that the variation distance between¯P T and the uniform distribution(or more generally,the limiting distribution lim T∞¯P T)is bounded by a sum over distinct pairs of eigenvalues,¯PT U 2T∑i j s tλiλja i2λiλj(4)where a iψ0v i is the component of the initial state along the eigenvector v i.(Since this bound includes eigenvaluesλj for which a j0,we note that it also holds when we replace a i2with a i a j,using the same reasoning as in[AAKV01].)For the quantum walk on the cycle of length n,this bound gives an average mixing time of O n log n. For the n-cube,however,there are exponentially many pairs of eigenvectors with distinct eigenvalues,all ofwhich have a non-zero component in the initial state.Speciﬁcally,for each Hamming weight k there are nk non-trivial eigenvectors each with eigenvalue e iωk and e iωk.These complex conjugates are distinct from each other for0k n,and eigenvalues with distinct k are also distinct.The number of distinct pairs is thenn1∑k1nk24n∑k k0nknkΩ4nTaking a k2n2from Equation1and the fact thatλiλj2since theλi are on the unit circle, we see that Equation4gives an upper bound on theε-average mixing time of sizeΩ2nε.In general,this bound will give a mixing time of O Mεwhenever the initial state is distributed roughly equally over M eigenvectors,and when these are roughly equally distributed overω1distinct eigenvalues.2.2The instantaneous mixing time of the discrete-time walkTo prove Theorem1we could calculateΨt x by Fourier transforming˜P t k back to real space for all x. However,this calculation turns out to be signiﬁcantly more awkward than calculating the Fourier trans-form of the probability distribution,˜P t k,which we need to apply the Diaconis-Shahshahani bound.Since P t xΨt xΨt x,and since multiplications in real space are convolutions in Fourier space,we perform a convolution over n2:˜Pt k∑k ˜Ψt k˜Ψt k kwhere the inner product is deﬁned on the direction space,u v∑n i1u i v i.We write this as a sum over j, the number of bits of overlap between k and k,and l,the number of bits of k outside the bits of k(and so overlapping with k k).Thus k has weight j l,and k k has weight k j l.Calculating the dot product˜Ψt k˜Ψt k k explicitly from Equation3as a function of these weights and overlaps gives˜P t k 12k∑j0n k∑l0kjn klcosωj l t cosωk j l t A sinωj l t sinωk j l t(5)whereA cosωk cosωj l cosωk j l sinωj l sinωk j lThe reader can check that this gives˜P t01for the trivial Fourier component where k0,and˜P t n 1t for the parity term where k n.Using the identities cos a cos b12cos a b cos a b and sin a sin b12cos a b cos a b we can re-write Equation5as˜P t k 12k∑j0n k∑l0kjn kl1A2cosωt1A2cosωt12k∑j0n k∑l0kjn klY(6)whereωωj lωk j l.The terms cosωt in Y are rapidly oscillating with a frequency that increases with t.Thus,unlike the walk on the cycle,the phase is rapidly oscillating everywhere,as a function of either l or j.This will make the dominant contribution to˜P t k exponentially small when t nπ4,giving us a small variation distance when we sum over all k.To give some intuition for the remainder of the proof,we pause here to note that if Equation6were an integral rather than a sum,we could immediately approximate the rate of oscillation of Y toﬁrst order at the peaks of the binomials,where j k2and l n k 2.One can check that dωk d k2n and hence dωd l dωd j4n.Since A1,we would then write˜Pt k O 12k∑j0n k∑l0kjn kle4i jt n e4ilt nwhich,using the binomial theorem,would give˜Pt k O 1e4it n2k1e4it n2n kcos k2tncos n k2tn(7)In this case the Diaconis-Shahshahani bound and the binomial theorem giveP t U214∑0k nnkcos k2tncos n k2tn2122cos22tnn1cos22tnn1If we could take t to be the non-integer valueπ4n,these cosines would be zero.This will,in fact,turn out to be the right answer.But since Equation6is a sum,not an integral,we have to be wary of resonances where the oscillations are such that the phase changes by a multiple of2πbetween adjacent terms,in which case these terms will interfere constructively rather than destructively.Thus to show that theﬁrst-order oscillation indeed dominates,we have a signiﬁcant amount of work left to do.The details of managing these resonances can be found in Appendix B.The process can be summarized as follows:i.)we compute the Fourier transform of the quantity Y in Equation6,since the sum of Equation6 can be calculated for a single Fourier basis function using the binomial theorem;ii.)the Fourier transform0.20.40.60.810.20.40.60.81(a)Variation distance at time t as a function of t n .(b)Log 2Probability as a function of Hamming weight.Figure 1:Graph (a)plots an exact calculation of the total variation distance after t steps of the quantum walk for hypercubes of dimension 50,100,and 200,as a function of t n .At t n π4the variation distance is small even though the walk has not had time to cross the entire graph.This happens because the distribution is roughly uniform across the equator of the n -cube where the vast majority of the points are located.Note that the window in which the variation distance is small gets narrower as n increases.Graph (b)shows the log 2probability distribution on the 200-dimensional hypercube as a function of Hamming distance from the starting point after 157π4n steps.The probability distribution has a plateau of 2199at the equator,matching the uniform distribution up to parity.of Y can be asymptotically bounded by the method of stationary phase.The dominant stationary point corresponds to the ﬁrst-order oscillation,but there are also lower-order stationary points corresponding to faster oscillations;so iii.)we use an entropy bound to show that the contribution of the other stationary points is exponentially small.To illustrate our result,we have calculated the probability distribution,and the total variation distance from the uniform distribution (up to parity),as a function of time for hypercubes of dimension 50,100,and 200.In order to do this exactly,we use the walk’s permutation symmetry to collapse its dynamics to a function only of Hamming distance.In Figure 1(a)we see that the total variation distance becomes small when t n π4,and in Figure 1(b)we see how the probability distribution is close to uniform on a “plateau”across the hypercube’s equator.Since this is where the vast majority of the points are located,the total variation distance is small even though the walk has not yet had time to cross the entire graph.3The continuous-time walkIn the case of the hypercube,the continuous-time walk turns out to be particularly easy to analyze.Theadjacency matrix,normalized by the degree,is H x y1n if x and y are adjacent,and 0otherwise.Interpreting H as the Hamiltonian treats it as the energy operator,and of course increasing the energy makes the system run faster;we normalize by the degree n in order to keep the maximum energy of the system,and so the rate at which transitions occur,constant as a function of n .The eigenvectors of H and U t are simply the Fourier basis functions:if v k x1k x then Hv k 12k n v k and U t v k e it 12k n v k where we again use k to denote the Hamming weight of k .If our initial wave vector has a particle at 0,then its initial Fourier spectrum is uniform,and at time t we have˜Ψt k 2n 2e it 12k n Again writing the probability P as the convolution of Ψwith Ψin Fourier space,。

219332006_超宽带太赫兹调频连续波成像技术

第 21 卷第 4 期2023 年 4 月Vol.21，No.4Apr.，2023太赫兹科学与电子信息学报Journal of Terahertz Science and Electronic Information Technology超宽带太赫兹调频连续波成像技术胡伟东，许志浩*，蒋环宇，刘庆国，檀桢(北京理工大学毫米波与太赫兹技术北京市重点实验室，北京100081)摘要：太赫兹调频连续波成像技术具有高功率、小型化、低成本、三维成像等特点，在太赫兹无损检测领域受到了广泛关注。

然而由于微波及太赫兹器件限制，太赫兹信号带宽难以做大，从而制约了成像的距离向分辨力。

虽然高载频可实现较大宽带，但伴随的低穿透性和低功率会限制太赫兹调频连续波成像系统的应用场景。

因此，聚焦于太赫兹波无损检测领域，提出一种时分频分复用的114~500 GHz超宽带太赫兹信号的产生方式，基于多频段共孔径准光设计，实现超带宽信号的共孔径，频率可扩展至1.1 THz。

提出一种频段融合算法，实现了超宽带信号的有效融合，距离分辨力提升至460 μm，通过人工设计的多层复合材料验证了系统及算法的有效性，并得到封装集成电路(IC)芯片的高分辨三维成像结果。

关键词：太赫兹调频连续波；非线性度校准；多频段融合；准光设计；无损检测中图分类号：TN914.42文献标志码：A doi：10.11805/TKYDA2022225Ultra-wideband terahertz FMCW imaging technologyHU Weidong，XU Zhihao*，JIANG Huanyu，LIU Qingguo，TAN Zhen (Beijing Key Laboratory of Millimeter Wave and Terahertz Technology，Beijing Institute of Technology，Beijing 100081，China)AbstractAbstract：：Terahertz Frequency Modulated Continuous Wave(THz FMCW) imaging technology has attracted extensive attention in the field of THz Nondestructive Testing(NDT) because of its high power,miniaturization, low cost, three-dimensional imaging and other characteristics. However, due to thelimitation of microwave and terahertz devices, the terahertz signal bandwidth is difficult to expand, whichrestricts the range resolution of imaging. Although high carrier frequency can achieve large broadband,the accompanying low penetrability and low power will limit the application scenario of THz FMCWimaging system. Therefore, focusing on the field of terahertz wave nondestructive testing, this paperproposes a time-division frequency-division multiplexing 114~500 GHz ultra-wideband terahertz signalgeneration method, which is based on the quasi-optical design of multiband common aperture to achievethe common aperture of ultra-wideband signals. In addition, a multiband fusion algorithm is proposed toachieve effective fusion of ultra-wideband signals, and the range resolution is improved to 460 μm. Theeffectiveness of the system and algorithm is verified by artificially designed multilayer compositematerials, and the high-resolution 3D imaging results of Integrated Circuit(IC) chips are obtained.KeywordsKeywords：：Terahertz Frequency Modulated Continuous Wave；non-linearity calibration；multiband fusion；quasi-optical design；Nondestructive Testing太赫兹波(0.03 mm~3 mm)在电磁波谱中位于微波与红外之间，由于其独特的穿透性与非电离性等特性，太赫兹技术已成功用于艺术品保护、工业产品质量控制、封装集成电路(IC)无损检测等领域[1-3]。

物理学名词

1/4波片quarter-wave plateCG矢量耦合系数Clebsch-Gordan vector coupling coefficient; 简称“CG[矢耦]系数”。

X射线摄谱仪X-ray spectrographX射线衍射X-ray diffractionX射线衍射仪X-ray diffractometer[玻耳兹曼]H定理[Boltzmann] H-theorem[玻耳兹曼]H函数[Boltzmann] H-function[彻]体力body force[冲]击波shock wave[冲]击波前shock front[狄拉克]δ函数[Dirac] δ-function[第二类]拉格朗日方程Lagrange equation[电]极化强度[electric] polarization[反射]镜mirror[光]谱线spectral line[光]谱仪spectrometer[光]照度illuminance[光学]测角计[optical] goniometer[核]同质异能素[nuclear] isomer[化学]平衡常量[chemical] equilibrium constant[基]元电荷elementary charge[激光]散斑speckle[吉布斯]相律[Gibbs] phase rule[可]变形体deformable body[克劳修斯-]克拉珀龙方程[Clausius-] Clapeyron equation[量子]态[quantum] state[麦克斯韦-]玻耳兹曼分布[Maxwell-]Boltzmann distribution[麦克斯韦-]玻耳兹曼统计法[Maxwell-]Boltzmann statistics[普适]气体常量[universal] gas constant[气]泡室bubble chamber[热]对流[heat] convection[热力学]过程[thermodynamic] process[热力学]力[thermodynamic] force[热力学]流[thermodynamic] flux[热力学]循环[thermodynamic] cycle[事件]间隔interval of events[微观粒子]全同性原理identity principle [of microparticles][物]态参量state parameter, state property[相]互作用interaction[相]互作用绘景interaction picture[相]互作用能interaction energy[旋光]糖量计saccharimeter[指]北极north pole, N pole[指]南极south pole, S pole[主]光轴[principal] optical axis[转动]瞬心instantaneous centre [of rotation][转动]瞬轴instantaneous axis [of rotation]t 分布student's t distributiont 检验student's t testＫ俘获K-captureＳ矩阵S-matrixＷＫＢ近似WKB approximationＸ射线X-rayΓ空间Γ-spaceα粒子α-particleα射线α-rayα衰变α-decayβ射线β-rayβ衰变β-decayγ矩阵γ-matrixγ射线γ-rayγ衰变γ-decayλ相变λ-transitionμ空间μ-spaceχ 分布chi square distributionχ 检验chi square test阿贝不变量Abbe invariant阿贝成象原理Abbe principle of image formation阿贝折射计Abbe refractometer阿贝正弦条件Abbe sine condition阿伏伽德罗常量Avogadro constant阿伏伽德罗定律Avogadro law阿基米德原理Archimedes principle阿特伍德机Atwood machine艾里斑Airy disk爱因斯坦-斯莫卢霍夫斯基理论Einstein-Smoluchowski theory 爱因斯坦场方程Einstein field equation爱因斯坦等效原理Einstein equivalence principle爱因斯坦关系Einstein relation爱因斯坦求和约定Einstein summation convention爱因斯坦同步Einstein synchronization爱因斯坦系数Einstein coefficient安[培]匝数ampere-turns安培[分子电流]假说Ampere hypothesis安培定律Ampere law安培环路定理Ampere circuital theorem安培计ammeter安培力Ampere force安培天平Ampere balance昂萨格倒易关系Onsager reciprocal relation凹面光栅concave grating凹面镜concave mirror凹透镜concave lens奥温电桥Owen bridge巴比涅补偿器Babinet compensator巴耳末系Balmer series白光white light摆pendulum板极plate伴线satellite line半波片halfwave plate半波损失half-wave loss半波天线half-wave antenna半导体semiconductor半导体激光器semiconductor laser半衰期half life period半透[明]膜semi-transparent film半影penumbra半周期带half-period zone傍轴近似paraxial approximation傍轴区paraxial region傍轴条件paraxial condition薄膜干涉film interference薄膜光学film optics薄透镜thin lens保守力conservative force保守系conservative system饱和saturation饱和磁化强度saturation magnetization本底background本体瞬心迹polhode本影umbra本征函数eigenfunction本征频率eigenfrequency本征矢[量] eigenvector本征振荡eigen oscillation本征振动eigenvibration本征值eigenvalue本征值方程eigenvalue equation比长仪comparator比荷specific charge; 又称“荷质比(charge-mass ratio)”。

孙昌璞 - 中国科学院理论物理研究所

CEV
Controlled Evolution
̃, 1 1
1,0 ̃ 3 p 1,1 S , D |1, 0 〈1, 0| p S , D 1 , 1
̃ p 0,1 S ,D 0, 1
̃ , 1 p 0,0 |0, 0 〈0, 0|. 0 S ,D
中国科学院理论物理研究所
正功条件与热机效率
Measurement do not lead to entropy increase
,1 1, 0 ρ ( 2) = p 1 S , D | 1, 0〉〈1, 0 | + p S , D | 1, 1〉〈1, 1 | 0 ,1 0, 0 + pS , D | 0,1〉〈 0, 1 | + p S , D | 0, 0〉〈 0, 0 | .
2. 固态量子计算与关联系统演化的动力学敏感性
Quan, Song, Liu, Zanardi, and Sun, Decay of Loschmidt Echo Enhanced by Quantum Criticality, Phys. Rev. Lett. 96, 140604 (2006)
3. 量子信息启发的未来量子器件
中国科学院理论物理研究所
量子信息载体的物理实现
Ion Traps, Photons Liquid NMR
Nuclear Spins in Semiconductors
相干性
可规模化
易控制
Cooper-pair box ，SQUID, Single Juction
约瑟芬森结
2002-2003年JJ Q-比特的相干性得到极大改进
|e
|g
0 or 1
Quantum State

Dissipative quantum phase transition in a quantum dot

a r X i v :c o n d -m a t /0602019v 2 [c o n d -m a t .m e s -h a l l ] 14 F eb 2006Dissipative quantum phase transition in a quantum dotL´a szl´o Borda 1,Gergely Zar´a nd 1,2,and D.Goldhaber-Gordon 31Department of Theoretical Physics and Research Group “Theory of Condensed Matter”of the Hungarian Academy of Sciences,Budapest University of Technology and Economics,Budafoki ´u t 8.H-1521Hungary2Institut f¨u r Theoretische Festk¨o rperphysik,Universit¨a t Karlsruhe,76128Karlsruhe,Germany3Physics Department and Geballe Laboratory for Advanced Materials,Stanford University,Stanford CA 94305,USA(Dated:February 5,2008)We study the transport properties of a quantum dot (QD)with highly resistive gate electrodes,and show that the QD displays a quantum phase transition analogous to the famous dissipative phase transition ﬁrst identiﬁed by S.Chakravarty [Phys.Rev.Lett.49,681-684(1982)];for a review see [A.J.Leggett et al.,Rev.Mod.Phys.59,1(1987)].At temperature T =0,the charge on the central island of a conventional QD changes smoothly as a function of gate voltage,due to quantum ﬂuctuations.However,for suﬃciently large gate resistance charge ﬂuctuations on the island can freeze out even at the degeneracy point,causing the charge on the island to change in sharp steps as a function of gate voltage.For R g <R C the steps remain smeared out by quantum ﬂuctuations.The Coulomb blockade peaks in conductance display anomalous scaling at intermediate temperatures,and at very low temperatures a sharp step develops in the QD conductance.The single electron transistor (SET)is one of the mostbasic mesoscopic devices:A conducting island or quan-tum dot is attached by tunnel barriers to two leads and a capacitively-coupled gate electrode sets the number of electrons on the dot.For low enough temperatures,T ≪E C ,charge ﬂuctuations of the dot are suppressed except when the gate is tuned to make two charge states nearly degenerate.At these “charge degeneracy points”the charge on the dot strongly ﬂuctuates.For typical metallic SETs with a very large number of tunneling modes quantum ﬂuctuations of the charge turn out to be suppressed at low temperatures [1,2,3].For semi-conducting SETs with single mode junctions ,however,quantum ﬂuctuations of the charge are important and broaden out the charging steps at low T :In the limit of vanishing level spacing,δǫ→0charge ﬂuctuations are described by the two-channel Kondo model [4],while for T ≪δǫone recovers the so-called “mixed valence”regime of the Anderson model [5].In the above discussion we neglected the eﬀect of Ohmic dissipation in the lead electrodes.While this has been extensively studied for SETs with a very large number of tunneling modes [2],there is much less known about the eﬀects of dissipation in the Kondo regime:In a recent paper Le Hur showed that,assuming a contin-uum of quantum levels on the SET and a single tunnel mode,coupling to a dissipative bath drastically modiﬁes the results of Ref.[4]:large enough dissipation drives a Kosterlitz-Thouless-type phase transition and leads to a complete suppression of charge ﬂuctuations even at the degeneracy point [6,7].However,for most semiconduct-ing devices the level spacing δǫcannot be neglected in comparison to temperature,and spin ﬂuctuations must also be considered.Here we shall therefore investigate the eﬀects of dissipation at temperatures far below the level spacing on the dot,T ≪δǫ,a more realistic low-temperature limit for typical semiconductor SETs.As weshow below,a dissipation-induced quantum phase tran-sition takes place for T ≪δǫas well,although with dif-ferent and more complicated properties due to the in-terplay of charge and spin ﬂuctuations,and at a larger dissipation strength (gate resistance)than that needed for δǫ→0[6,7,8].In this T ≪δǫregime,the coupling of the quantum dot to the gate voltage is usually described by the Hamil-tonian,H dot =E C σd †σd σ−n g 2,(1)where E C ≡e 2/2C Σdenotes the charging energy,withC Σthe total capacitance of the dot,and e the electron charge.We retain only one single-particle level d ,and we assume that it is empty or singly occupied,depend-ing on the dimensionless gate voltage,n g [9].Assuming weak coupling between the dot and the source and drain electrodes,charge transfer can be described within the tunneling approximation,H tun =V σdǫσd †σψσ(ǫ)+h .c . ,(2)were ψσ(ǫ)annihilates an appropriate linear combinationof left and right lead electrons of energy ǫthat hybridize with the dot state d σ,and satisﬁes the anticommutation relation {ψσ(ǫ),ψσ′(ǫ′)}=δσσ′δ(ǫ−ǫ′)[10].Throughout this paper we assume that the quantum dot is close to symmetrical but our analysis carries over easily to asym-metrical dots as well.Eqs.(1)and (2)are thought to provide a satisfactory description of the SET for T ≪δǫfor most experimen-tal situations studied so far,including the Kondo regime [5].However,Eq.(1)does not account for the relax-ation of electrostatic charges in the nearby electrodes:in reality,when an electron tunnels into the dot,an elec-trostatic charge δQ =eC g /C Σis also generated on thegate.Transferring this charge from the outside world to the gate electrode throughashunt resistorrequirestime,andcreatesdissipation [11].Consequently,tunnelingbe-tweendotandleadswill be suppressed by Anderson’s orthogonality catastrophe.The simplest way to account for this shunt resistance is to add a term [1]H diss=λ ˆn −24C 2ΣR g2i,α,βS i (ψ†ασiαβψβ),(6)where the spin operators denote S i =1dl=14v +...,(7)djdl =−31dl=˜∆−32πδǫ≈v 2=22−ln α(0)c +13v +v 2+...,and the transition isof Kosterlitz-Thouless type [19]:On the localized side,α>α(0)c (or Γ<Γ(0)c ),at the degeneracy point the height δG of Coulomb blockade peaks scales to zero as a power law [18],δG (T )δǫ 2α∞−1(12)with G Q the quantum conductance.On the metallicside,on the other hand,quantum ﬂuctuations always dominate and preserve conductance even at T =0,though near the transition the conductance shows a non-monotonic behavior:δG (T )ﬁrst slowly decays and then starts to increase below a temperature T ∗that vanishes exponentially as one approaches the phase transition,αFIG.1:Schematic phase diagram of the SET in the presence of dissipative coupling.αc denotes the critical value ofα, whileα(0)c is its value obtained by neglecting the generated exchange coupling j.Forα>αc there is a phase transition from n =0to n =1,while in the more familiar situation of weak dissipation there is a crossover.T∗≈δǫexp{−π/2(α(0)c2−α2)1/2},untilﬁnally a mixed valence state with a large conductance is formed at a temperature T∗∗∼T∗2/δǫ≪T∗.For the critical value ofα,δG decays to zero logarithmically,1δG(T,α=α(0)c)∼G Q4−∆/δε0.51n >FIG.2:Charging steps,computed using NRG for a relatively small hybridization.For these parameters T K /δǫ∼10−10at α≈αc .Inset:Temperature dependence of the occu-pation number ˆn at the critical dissipation,α≈αc ,for ∆/δǫ=−0.0028800,−0.0028300,−0.0028200,−0.0028198,−0.0028190,−0.0028140,−0.0028000(bottom to top).order of α≈1can be reached in this way.The SET can be then tuned through the quantum phase transition by either continuously changing the tunneling V ,or by depleting a second 2DEG positioned below the dot and thereby changing the total capacitance of the dot and hence the value of α.In summary,we have shown that suﬃciently strong dis-sipation in the gate electrodes can drive the SET through a quantum phase transition into a state where charge de-grees of freedom become localized while spin ﬂuctuations lead to a Kondo eﬀect.In this state both the conductance and the expectation value of the charge on the SET dis-play a jump at temperature T =0,while at higher tem-1010−510−310−1ω/δε10−210−110R e [G (ω)]/G 0−0.0042400−0.0042450−0.0042460−0.0042500∆/δε=FIG.3:T =0AC conductivity of the SET in the localized phase for α=0.75and Γ/δǫ=0.5(G 0∼G Q ).peratures an anomalous scaling of the Coulomb blockade peaks is predicted.We estimate that this quantum phase transition can be detected by coupling a highly resistive gate electrode to a SET in a shallow 2DEG.We are grateful to P.Simon,K.Le Hur,Q.Si,O.Sauret,A.Zaikin and Y.Nazarov for valuable discus-sions.This research has been supported by NSF-MTA-OTKA Grant No.INT-0130446,Hungarian Grants Nos.T046303,NF061726,D048665,and T048782,the Euro-pean ’Spintronics’RTN HPRN-CT-2002-00302,and at Stanford University by NSF CAREER Award DMR-0349354and a Packard Fellowship.L.B.is a grantee of the J´a nos Bolyai Scholarship.[1]For early reviews,see e.g.G.Sch¨o n and A.D.Zaikin,Phys.Rep.198,237(1990),or G.-L.Ingold and Y.V.Nazarov,in:Single Charge Tunneling,ed.by H.Grabert and M.Devoret,NATO ASI Series B,vol.294,pp.21-107(Plenum,1992).[2]See also:S.V.Panyukov and A.D.Zaikin,Phys.Rev.Lett.67,3168(1991);G.Falci,G.Sch¨o n,and G.T.Zi-manyi,Phys.Rev.Lett.74,3257(1995);M.Kindermann and Yu.V.Nazarov,Phys.Rev.Lett.91,136802(2003).[3]P.Joyez et al.,Phys.Rev.Lett.79,1349-1352(1997);D.Chouvaev et al.,Phys.Rev.B 59,10599(1999);C.Wallisser et al.,Phys.Rev.B 66,125314(2002).[4]K.A.Matveev,Phys.Rev.B 51,1743(1995).[5]T.A.Costi,Phys.Rev.B 64,241310(R)(2001).[6]K.Le Hur,Phys.Rev.Lett.92,196804(2004).[7]L.Borda,G.Zarand,and P.Simon,Phys.Rev.B 72,155311(2005);M.-R.Li,K.Le Hur,and W.Hofstetter,Phys.Rev.Lett.95,086406(2005).[8]It has been argued earlier based on calculations for a sim-ple spinless model that the dissipative transition should survive even in this limit:K.Le Hur and M.-R.Li Phys.Rev.B 72,073305(2005).[9]The analysis would be very similar for the transition be-tween a singly-and doubly-occupied state.[10]With this normalization V ∼̺1/20,with ̺0the density ofstates in the leads.[11]We shall neglect dissipation on source and drain elec-trodes which we assume not to be highly resistive.[12]The constant 2/3appears naturally along the calcula-tions and is related to the (classical)expectation value of the charge at the degeneracy point.[13]M.H.Devoret et al.,Phys.Rev.Lett.64,1824(1990);S.M.Girvin,et al.,Phys.Rev.Lett.64,3183-3186(1990).[14]J.von Delft and H.Schoeller,Annalen Phys.7,225(1998).[15]J.Cardy,Scaling and Renormalization in StatisticalPhysics (Cambridge University Press,Cambridge,1996).[16]Q.Si and G.Kotliar,Phys.Rev.Lett.70,3143(1993).[17]The scaling equation for ˜∆in Ref.16breaks SU(2)in-variance,and some care is needed.[18]G.Zar´a nd et al.,unpublished.[19]J.M.Kosterlitz,J.Phys.C 7,1046(1974).[20]H.R.Krishna-murthy et al.,Phys.Rev.B 21,1003(1980).[21]G.Kotliar and Q.Si,Phys.Rev.B 53,12373(1996).5[22]P.Nozi`e res,J.Low Temp.Phys.17,31(1974).[23]Slightly below the critical couplingα(0)c,the tunnelingv is suppressed so much that the Kondo scale becomes larger than the mixed valence scale T∗∗.At the Kondo ﬁxed point,however,the tunneling becomes marginal,and smaller values ofαare suﬃcient to localize charge ﬂuctuations.Note that Eq.(7)is inappropriate in this Kondo regime,and a strong coupling analysis is needed to obtain the above picture.。

Quantum Mechanics

Quantum MechanicsQuantum Mechanics is the branch of physics that deals with the behavior of matter and energy at a microscopic level. It is a complex andfascinating subject that has revolutionized our understanding of the universe. Quantum Mechanics is based on the principles of quantum theory, which describes the behavior of particles at the subatomic level.One of the most important concepts in Quantum Mechanics is the wave-particle duality. This principle states that particles can behave as both waves and particles at the same time. This means that electrons, for example, can exist in multiple places at once and can interfere with themselves. This idea is fundamental to Quantum Mechanics and has led to many of its most important discoveries.Another important concept in Quantum Mechanics is the uncertainty principle. This principle states that it is impossible to know both the position and momentum of a particle at the same time. The more precisely we know the position of a particle, the less precisely we can know its momentum, and vice versa. This principle has important implications for the behavior of particles at the subatomic level.Quantum Mechanics has many practical applications, including in the development of new technologies such as transistors and lasers. It is also important in the study of materials and the behavior of atoms and molecules. Quantum Mechanics has led to many breakthroughs in our understanding of the universe and has helped us to develop new technologies that havetransformed our world.However, Quantum Mechanics is also a subject that is often misunderstood and can be difficult to grasp. The concepts involved are very different from our everyday experience, and the mathematics can be complex and abstract. This can make it challenging for students to learn and for researchers to make progress in the field.One of the challenges of Quantum Mechanics is that it seems to contradict our everyday experience of the world. For example, the idea that particles can exist in multiple places at once seems to go against our intuition. However, this is a fundamental principle of Quantum Mechanics, and experiments have shown that it is true.Another challenge of Quantum Mechanics is that the mathematics involved can be very complex and abstract. This can make it difficult for students to learn and for researchers to make progress in the field. However, the mathematics is essential for understanding the behavior of particles at the subatomic level, and it has led to many important discoveries in the field.Despite the challenges, Quantum Mechanics is a fascinating subject that has revolutionized our understanding of the universe. It has led to many important discoveries and has helped us to develop new technologies that have transformed our world. While it may be difficult to grasp at first, with time and effort, anyone can learn about this important field of physics.。

半无限深势阱中自旋相关玻色-爱因斯坦凝聚体的量子反射与

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Quantum Walk on the Line (Extended Abstract)

1
Introduction
Random walks on graphs have found many applications in computer science, including randomised algorithms for 2-Satisﬁability, Graph Connectivity and probability ampliﬁcation (see, e.g., [14]). Recently, Sch¨ oning [19] discovered a random walk based algorithm similar to that of Papadimitriou [17] that gives an elegant (and the most eﬃcient known) solution to 3-Satisﬁability. In general, Markov chain simulation has emerged as a powerful algorithmic tool and has had a profound impact on random sampling and approximate counting [10]. Notable among its numerous applications are estimating the volume of convex bodies [6]1 and approximating the permanent [9]. A few months ago, Jerrum, Sinclair and Vigoda [11] used this approach to solve the long standing open problem of approximating the permanent for general non-negative matrices. In the spirit of developing similar techniques for quantum algorithms, we consider quantum walk on graphs. To date, few general techniques are known for developing and analysing quantum algorithms: Fourier sampling, which is typiﬁed by the seminal work of Simon [21] and Shor [20], and amplitude ampliﬁcation, which originated in the seminal work of Grover [8]. Barring applications of these techniques, the search for

第十八届全国凝聚态理论与统计物理学术会议

目录
1．会议日程简表 2．会议详细日程安排 3．大会邀请报告、分会邀请报告、分会一般报告和张贴报告编码规则 4．大会邀请报告: 题目与摘要 5．分会邀请报告和一般报告: 题目与摘要 6．张贴报告: 题目与摘要 7．通讯录
第十八届全国凝聚态理论与统计物理学术会议
日
日期 2014 年 7 月 26 日 2014 年 7 月 27 日时间全天签到、注册
午餐&小憩地点：重庆大学学生第 1 食堂 2 楼大厅（见校园引导标识、或会议相关地图）
2014 年 7 月 27 日第二单元：分会报告（第一分会场）地点：民主湖报告厅 13:30-14:00 主题：1 主持人：罗洪刚（兰州大学）
分会邀请报告：Three Component Ultracold Fermi Gases Under Spin-orbit Coupling 报告人：易为（中国科技大学）
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近藤效应

Tunable Kondo eﬀect in a single donor atomnsbergen 1,G.C.Tettamanzi 1,J.Verduijn 1,N.Collaert 2,S.Biesemans 2,M.Blaauboer 1,and S.Rogge 11Kavli Institute of Nanoscience,Delft University of Technology,Lorentzweg 1,2628CJ Delft,The Netherlands and2InterUniversity Microelectronics Center (IMEC),Kapeldreef 75,3001Leuven,Belgium(Dated:September 30,2009)The Kondo eﬀect has been observed in a single gate-tunable atom.The measurement device consists of a single As dopant incorporated in a Silicon nanostructure.The atomic orbitals of the dopant are tunable by the gate electric ﬁeld.When they are tuned such that the ground state of the atomic system becomes a (nearly)degenerate superposition of two of the Silicon valleys,an exotic and hitherto unobserved valley Kondo eﬀect appears.Together with the “regular”spin Kondo,the tunable valley Kondo eﬀect allows for reversible electrical control over the symmetry of the Kondo ground state from an SU(2)-to an SU(4)-conﬁguration.The addition of magnetic impurities to a metal leads to an anomalous increase of their resistance at low tem-perature.Although discovered in the 1930’s,it took until the 1960’s before this observation was satisfactorily ex-plained in the context of exchange interaction between the localized spin of the magnetic impurity and the de-localized conduction electrons in the metal [1].This so-called Kondo eﬀect is now one of the most widely stud-ied phenomena in condensed-matter physics [2]and plays a mayor role in the ﬁeld of nanotechnology.Kondo ef-fects on single atoms have ﬁrst been observed by STM-spectroscopy and were later discovered in a variety of mesoscopic devices ranging from quantum dots and car-bon nanotubes to single molecules [3].Kondo eﬀects,however,do not only arise from local-ized spins:in principle,the role of the electron spin can be replaced by another degree of freedom,for example or-bital momentum [4].The simultaneous presence of both a spin-and an orbital degeneracy gives rise to an exotic SU(4)-Kondo eﬀect,where ”SU(4)”refers to the sym-metry of the corresponding Kondo ground state [5,6].SU(4)Kondo eﬀects have received quite a lot of theoret-ical attention [6,7],but so far little experimental work exists [8].The atomic orbitals of a gated donor in Si consist of linear combinations of the sixfold degenerate valleys of the Si conduction band.The orbital-(or more speciﬁ-cally valley)-degeneracy of the atomic ground state is tunable by the gate electric ﬁeld.The valley splitting ranges from ∼1meV at high ﬁelds (where the electron is pulled towards the gate interface)to being equal to the donors valley-orbit splitting (∼10-20meV)at low ﬁelds [9,10].This tunability essentially originates from a gate-induced quantum conﬁnement transition [10],namely from Coulombic conﬁnement at the donor site to 2D-conﬁnement at the gate interface.In this article we study Kondo eﬀects on a novel exper-imental system,a single donor atom in a Silicon nano-MOSFET.The charge state of this single dopant can be tuned by the gate electrode such that a single electron (spin)is localized on the pared to quantum dots (or artiﬁcial atoms)in Silicon [11,12,13],gated dopants have a large charging energy compared to the level spac-ing due to their typically much smaller size.As a result,the orbital degree of freedom of the atom starts to play an important role in the Kondo interaction.As we will argue in this article,at high gate ﬁeld,where a (near)de-generacy is created,the valley index forms a good quan-tum number and Valley Kondo [14]eﬀects,which have not been observed before,appear.Moreover,the Valley Kondo resonance in a gated donor can be switched on and oﬀby the gate electrode,which provides for an electri-cally controllable quantum phase transition [15]between the regular SU(2)spin-and the SU(4)-Kondo ground states.In our experiment we use wrap-around gate (FinFET)devices,see Fig.1(a),with a single Arsenic donor in the channel dominating the sub-threshold transport charac-teristics [16].Several recent experiments have shown that the ﬁngerprint of a single dopant can be identiﬁed in low-temperature transport through small CMOS devices [16,17,18].We perform transport spectroscopy (at 4K)on a large ensemble of FinFET devices and select the few that show this ﬁngerprint,which essentially consists of a pair of characteristic transport resonances associ-ated with the one-electron (D 0)-and two-electron (D −)-charge states of the single donor [16].From previous research we know that the valley splitting in our Fin-FET devices is typically on the order of a few meV’s.In this Report,we present several such devices that are in addition characterized by strong tunnel coupling to the source/drain contacts which allows for suﬃcient ex-change processes between the metallic contacts and the atom to observe Kondo eﬀects.Fig.1b shows a zero bias diﬀerential conductance (dI SD /dV SD )trace at 4.2K as a function of gate volt-age (V G )of one of the strongly coupled FinFETs (J17).At the V G such that a donor level in the barrier is aligned with the Fermi energy in the source-drain con-tacts (E F ),electrons can tunnel via the level from source to drain (and vice versa)and we observe an increase in the dI SD /dV SD .The conductance peaks indicated bya r X i v :0909.5602v 1 [c o n d -m a t .m e s -h a l l ] 30 S e p 2009FIG.1:Coulomb blocked transport through a single donor in FinFET devices(a)Colored Scanning Electron Micrograph of a typical FinFET device.(b)Diﬀerential conductance (dI SD/dV SD)versus gate voltage at V SD=0.(D0)and(D−) indicate respectively the transport resonances of the one-and two-electron state of a single As donor located in the Fin-FET channel.Inset:Band diagram of the FinFET along the x-axis,with the(D0)charge state on resonance.(c)and(d) Colormap of the diﬀerential conductance(dI SD/dV SD)as a function of V SD and V G of samples J17and H64.The red dots indicate the(D0)resonances and data were taken at1.6 K.All the features inside the Coulomb diamonds are due to second-order chargeﬂuctuations(see text).(D0)and(D−)are the transport resonances via the one-electron and two-electron charge states respectively.At high gate voltages(V G>450mV),the conduction band in the channel is pushed below E F and the FET channel starts to open.The D−resonance has a peculiar double peak shape which we attribute to capacitive coupling of the D−state to surrounding As atoms[19].The current between the D0and the D−charge state is suppressed by Coulomb blockade.The dI SD/dV SD around the(D0)and(D−)resonances of sample J17and sample H64are depicted in Fig.1c and Fig.1d respectively.The red dots indicate the po-sitions of the(D0)resonance and the solid black lines crossing the red dots mark the outline of its conducting region.Sample J17shows aﬁrst excited state at inside the conducting region(+/-2mV),indicated by a solid black line,associated with the valley splitting(∆=2 mV)of the ground state[10].The black dashed lines indicate V SD=0.Inside the Coulomb diamond there is one electron localized on the single As donor and all the observable transport in this regionﬁnds its origin in second-order exchange processes,i.e.transport via a vir-tual state of the As atom.Sample J17exhibits three clear resonances(indicated by the dashed and dashed-dotted black lines)starting from the(D0)conducting region and running through the Coulomb diamond at-2,0and2mV. The-2mV and2mV resonances are due to a second or-der transition where an electron from the source enters one valley state,an the donor-bound electron leaves from another valley state(see Fig.2(b)).The zero bias reso-nance,however,is typically associated with spin Kondo eﬀects,which happen within the same valley state.In sample H64,the pattern of the resonances looks much more complicated.We observe a resonance around0mV and(interrupted)resonances that shift in V SD as a func-tion of V G,indicating a gradual change of the internal level spectrum as a function of V G.We see a large in-crease in conductance where one of the resonances crosses V SD=0(at V G∼445mV,indicated by the red dashed elipsoid).Here the ground state has a full valley degen-eracy,as we will show in theﬁnal paragraph.There is a similar feature in sample J17at V G∼414mV in Fig.1c (see also the red cross in Fig.1b),although that is prob-ably related to a nearby defect.Because of the relative simplicity of its diﬀerential conductance pattern,we will mainly use data obtained from sample J17.In order to investigate the behavior at the degeneracy point of two valley states we use sample H64.In the following paragraphs we investigate the second-order transport in more detail,in particular its temper-ature dependence,ﬁne-structure,magneticﬁeld depen-dence and dependence on∆.We start by analyzing the temperature(T)dependence of sample J17.Fig.2a shows dI SD/dV SD as a function of V SD inside the Coulomb diamond(at V G=395mV) for a range of temperatures.As can be readily observed from Fig.2a,both the zero bias resonance and the two resonances at V SD=+/-∆mV are suppressed with increasing T.The inset of Fig.2a shows the maxima (dI/dV)MAX of the-2mV and0mV resonances as a function of T.We observe a logarithmic dependence on T(a hallmark sign of Kondo correlations)at both resonances,as indicated by the red line.To investigate this point further we analyze another sample(H67)which has sharper resonances and of which more temperature-dependent data were obtained,see Fig.2c.This sample also exhibits the three resonances,now at∼-1,0and +1mV,and the same strong suppression by tempera-ture.A linear background was removed for clarity.We extracted the(dI/dV)MAX of all three resonances forFIG.2:Electrical transport through a single donor atom in the Coulomb blocked region(a)Diﬀerential conductance of sample J17as a function of V SD in the Kondo regime(at V G=395mV).For clarity,the temperature traces have been oﬀset by50nS with respect to each other.Both the resonances with-and without valley-stateﬂip scale similarly with increasing temperature. Inset:Conductance maxima of the resonances at V SD=-2mV and0mV as a function of temperature.(b)Schematic depiction of three(out of several)second-order processes underlying the zero bias and±∆resonances.(c)Diﬀerential conductance of sample H67as a function of V SD in the Kondo regime between0.3K and6K.A linear(and temperature independent) background on the order of1µS was removed and the traces have been oﬀset by90nS with respect to each other for clarity.(d)The conductance maxima of the three resonances of(c)normalized to their0.3K value.The red line is aﬁt of the data by Eq.1.all temperatures and normalized them to their respective(dI/dV)MAX at300mK.The result is plotted in Fig.2d.We again observe that all three peaks have the same(log-arithmic)dependence on temperature.This dependenceis described well by the following phenomenological rela-tionship[20](dI SD/dV SD)max (T)=(dI SD/dV SD)T 2KT2+TKs+g0(1)where TK =T K/√21/s−1,(dI SD/dV SD)is the zero-temperature conductance,s is a constant equal to0.22 [21]and g0is a constant.Here T K is the Kondo tem-perature.The red curve in Fig.2d is aﬁt of Eq.(1)to the data.We readily observe that the dataﬁt well and extract a T K of2.7K.The temperature scaling demon-strates that both the no valley-stateﬂip resonance at zero bias voltage and the valley-stateﬂip-resonance atﬁnite bias are due to Kondo-type processes.Although a few examples ofﬁnite-bias Kondo have been reported[15,22,23],the corresponding resonances (such as our±∆resonances)are typically associated with in-elastic cotunneling.Aﬁnite bias between the leads breaks the coherence due to dissipative transitions in which electrons are transmitted from the high-potential-lead to the low-potential lead[24].These dissipative4transitions limit the lifetime of the Kondo-type processes and,if strong enough,would only allow for in-elastic events.In the supporting online text we estimate the Kondo lifetime in our system and show it is large enough to sustain theﬁnite-bias Kondo eﬀects.The Kondo nature of the+/-∆mV resonances points strongly towards a Valley Kondo eﬀect[14],where co-herent(second-order)exchange between the delocalized electrons in the contacts and the localized electron on the dopant forms a many-body singlet state that screens the valley index.Together with the more familiar spin Kondo eﬀect,where a many-body state screens the spin index, this leads to an SU(4)-Kondo eﬀect,where the spin and charge degree of freedom are fully entangled[8].The ob-served scaling of the+/-∆-and zero bias-resonances in our samples by a single T K is an indication that such a fourfold degenerate SU(4)-Kondo ground state has been formed.To investigate the Kondo nature of the transport fur-ther,we analyze the substructure of the resonances of sample J17,see Fig.2a.The central resonance and the V SD=-2mV each consist of three separate peaks.A sim-ilar substructure can be observed in sample H67,albeit less clear(see Fig.2c).The substructure can be explained in the context of SU(4)-Kondo in combination with a small diﬀerence between the coupling of the ground state (ΓGS)-and theﬁrst excited state(ΓE1)-to the leads.It has been theoretically predicted that even a small asym-metry(ϕ≡ΓE1/ΓGS∼=1)splits the Valley Kondo den-sity of states into an SU(2)-and an SU(4)-part[25].Thiswill cause both the valley-stateﬂip-and the no valley-stateﬂip resonances to split in three,where the middle peak is the SU(2)-part and the side-peaks are the SU(4)-parts.A more detailed description of the substructure can be found in the supporting online text.The split-ting between middle and side-peaks should be roughly on the order of T K[25].The measured splitting between the SU(2)-and SU(4)-parts equals about0.5meV for sample J17and0.25meV for sample H67,which thus corresponds to T K∼=6K and T K∼=3K respectively,for the latter in line with the Kondo temperature obtained from the temperature dependence.We further note that dI SD/dV SD is smaller than what we would expect for the Kondo conductance at T<T K.However,the only other study of the Kondo eﬀect in Silicon where T K could be determined showed a similar magnitude of the Kondo signal[12].The presence of this substructure in both the valley-stateﬂip-,and the no valley-stateﬂip-Kondo resonance thus also points at a Valley Kondo eﬀect.As a third step,we turn our attention to the magnetic ﬁeld(B)dependence of the resonances.Fig.3shows a colormap plot of dI SD/dV SD for samples J17and H64 both as a function of V SD and B at300mK.The traces were again taken within the Coulomb diamond.Atﬁnite magneticﬁeld,the central Kondo resonances of both de-vices split in two with a splitting of2.2-2.4mV at B=FIG.3:Colormap plot of the conductance as a function of V SD and B of sample J17at V G=395mV(a)and H64at V G=464mV(b).The central Kondo resonances split in two lines which are separated by2g∗µB B.The resonances with a valley-stateﬂip do not seem to split in magneticﬁeld,a feature we associate with the diﬀerent decay-time of parallel and anti-parallel spin-conﬁgurations of the doubly-occupied virtual state(see text).10T.From theoretical considerations we expect the cen-tral Valley Kondo resonance to split in two by∆B= 2g∗µB B if there is no mixing of valley index(this typical 2g∗µB B-splitting of the resonances is one of the hall-marks of the Kondo eﬀect[24]),and to split in three (each separated by g∗µB B)if there is a certain degree of valley index mixing[14].Here,g∗is the g-factor(1.998 for As in Si)andµB is the Bohr magneton.In the case of full mixing of valley index,the valley Kondo eﬀect is expected to vanish and only spin Kondo will remain [25].By comparing our measured magneticﬁeld splitting (∆B)with2g∗µB B,weﬁnd a g-factor between2.1and 2.4for all three devices.This is comparable to the result of Klein et al.who found a g-factor for electrons in SiGe quantum dots in the Kondo regime of around2.2-2.3[13]. The magneticﬁeld dependence of the central resonance5indicates that there is no signiﬁcant mixing of valley in-dex.This is an important observation as the occurrence of Valley Kondo in Si depends on the absence of mix-ing(and thus the valley index being a good quantum number in the process).The conservation of valley in-dex can be attributed to the symmetry of our system. The large2D-conﬁnement provided by the electricﬁeld gives strong reason to believe that the ground-andﬁrst excited-states,E GS and E1,consist of(linear combi-nations of)the k=(0,0,±kz)valleys(with z in the electricﬁeld direction)[10,26].As momentum perpen-dicular to the tunneling direction(k x,see Fig.1)is con-served,also valley index is conserved in tunneling[27]. The k=(0,0,±k z)-nature of E GS and E1should be as-sociated with the absence of signiﬁcant exchange interac-tion between the two states which puts them in the non-interacting limit,and thus not in the correlated Heitler-London limit where singlets and triplets are formed.We further observe that the Valley Kondo resonances with a valley-stateﬂip do not split in magneticﬁeld,see Fig.3.This behavior is seen in both samples,as indicated by the black straight solid lines,and is most easily ob-served in sample J17.These valley-stateﬂip resonances are associated with diﬀerent processes based on their evo-lution with magneticﬁeld.The processes which involve both a valleyﬂip and a spinﬂip are expected to shift to energies±∆±g∗µB B,while those without a spin-ﬂip stay at energies±∆[14,25].We only seem to observe the resonances at±∆,i.e.the valley-stateﬂip resonances without spinﬂip.In Ref[8],the processes with both an orbital and a spinﬂip also could not be observed.The authors attribute this to the broadening of the orbital-ﬂip resonances.Here,we attribute the absence of the processes with spinﬂip to the diﬀerence in life-time be-tween the virtual valley state where two spins in seperate valleys are parallel(τ↑↑)and the virtual state where two spins in seperate valleys are anti-parallel(τ↑↓).In con-trast to the latter,in the parallel spin conﬁguration the electron occupying the valley state with energy E1,can-not decay to the other valley state at E GS due to Pauli spin blockade.It wouldﬁrst needs toﬂip its spin[28].We have estimatedτ↑↑andτ↑↓in our system(see supporting online text)andﬁnd thatτ↑↑>>h/k b T K>τ↑↓,where h/k b T K is the characteristic time-scale of the Kondo pro-cesses.Thus,the antiparallel spin conﬁguration will have relaxed before it has a change to build up a Kondo res-onance.Based on these lifetimes,we do not expect to observe the Kondo resonances associated with both an valley-state-and a spin-ﬂip.Finally,we investigate the degeneracy point of valley states in the Coulomb diamond of sample H64.This degeneracy point is indicated in Fig.1d by the red dashed ellipsoid.By means of the gate electrode,we can tune our system onto-or oﬀthis degeneracy point.The gate-tunability in this sample is created by a reconﬁguration of the level spectrum between the D0and D−-charge states,FIG.4:Colormap plot of I SD at V SD=0as a function of V G and B.For increasing B,a conductance peak develops around V G∼450mV at the valley degeneracy point(∆= 0),indicated by the dashed black line.Inset:Magneticﬁeld dependence of the valley degeneracy point.The resonance is ﬁxed at zero bias and its magnitude does not depend on the magneticﬁeld.probably due to Coulomb interactions in the D−-states. Figure4shows a colormap plot of I SD at V SD=0as a function of V G and B(at0.3K).Note that we are thus looking at the current associated with the central Kondo resonance.At B=0,we observe an increasing I SD for higher V G as the atom’s D−-level is pushed toward E F. As B is increased,the central Kondo resonance splits and moves away from V SD=0,see Fig.3.This leads to a general decrease in I SD.However,at around V G= 450mV a peak in I SD develops,indicated by the dashed black line.The applied B-ﬁeld splits oﬀthe resonances with spin-ﬂip,but it is the valley Kondo resonance here that stays at zero bias voltage giving rise to the local current peak.The inset of Fig.4shows the single Kondo resonance in dI SD/dV SD as a function of V SD and B.We observe that the magnitude of the resonance does not decrease signiﬁcantly with magneticﬁeld in contrast to the situation at∆=0(Fig.3b).This insensitivity of the Kondo eﬀect to magneticﬁeld which occurs only at∆= 0indicates the profound role of valley Kondo processes in our structure.It is noteworthy to mention that at this speciﬁc combination of V SD and V G the device can potentially work as a spin-ﬁlter[6].We acknowledge fruitful discussions with Yu.V. Nazarov,R.Joynt and S.Shiau.This project is sup-ported by the Dutch Foundation for Fundamental Re-search on Matter(FOM).6[1]Kondo,J.,Resistance Minimum in Dilute Magnetic Al-loys,Prog.Theor.Phys.3237-49(1964)[2]Hewson,A.C.,The Kondo Problem to Heavy Fermions(Cambridge Univ.Press,Cambridge,1993).[3]Wingreen N.S.,The Kondo eﬀect in novel systems,Mat.Science Eng.B842225(2001)and references therein.[4]Cox,D.L.,Zawadowski,A.,Exotic Kondo eﬀects in met-als:magnetic ions in a crystalline electricﬁeld and tun-neling centers,Adv.Phys.47,599-942(1998)[5]Inoshita,T.,Shimizu, A.,Kuramoto,Y.,Sakaki,H.,Correlated electron transport through a quantum dot: the multiple-level eﬀect.Phys.Rev.B48,14725-14728 (1993)[6]Borda,L.Zar´a nd,G.,Hofstetter,W.,Halperin,B.I.andvon Delft,J.,SU(4)Fermi Liquid State and Spin Filter-ing in a Double Quantum Dot System,Phys.Rev.Lett.90,026602(2003)[7]Zar´a nd,G.,Orbitalﬂuctuations and strong correlationsin quantum dots,Philosophical Magazine,86,2043-2072 (2006)[8]Jarillo-Herrero,P.,Kong,J.,van der Zant H.S.J.,Dekker,C.,Kouwenhoven,L.P.,De Franceschi,S.,Or-bital Kondo eﬀect in carbon nanotubes,Nature434,484 (2005)[9]Martins,A.S.,Capaz,R.B.and Koiller,B.,Electric-ﬁeldcontrol and adiabatic evolution of shallow donor impuri-ties in silicon,Phys.Rev.B69,085320(2004)[10]Lansbergen,G.P.et al.,Gate induced quantum conﬁne-ment transition of a single dopant atom in a Si FinFET, Nature Physics4,656(2008)[11]Rokhinson,L.P.,Guo,L.J.,Chou,S.Y.,Tsui, D.C.,Kondo-like zero-bias anomaly in electronic transport through an ultrasmall Si quantum dot,Phys.Rev.B60, R16319-R16321(1999)[12]Specht,M.,Sanquer,M.,Deleonibus,S.,Gullegan G.,Signature of Kondo eﬀect in silicon quantum dots,Eur.Phys.J.B26,503-508(2002)[13]Klein,L.J.,Savage, D.E.,Eriksson,M.A.,Coulombblockade and Kondo eﬀect in a few-electron silicon/silicon-germanium quantum dot,Appl.Phys.Lett.90,033103(2007)[14]Shiau,S.,Chutia,S.and Joynt,R.,Valley Kondo eﬀectin silicon quantum dots,Phys.Rev.B75,195345(2007) [15]Roch,N.,Florens,S.,Bouchiat,V.,Wernsdirfer,W.,Balestro, F.,Quantum phase transistion in a single molecule quantum dot,Nature453,633(2008)[16]Sellier,H.et al.,Transport Spectroscopy of a SingleDopant in a Gated Silicon Nanowire,Phys.Rev.Lett.97,206805(2006)[17]Calvet,L.E.,Wheeler,R.G.and Reed,M.A.,Observa-tion of the Linear Stark Eﬀect in a Single Acceptor in Si, Phys.Rev.Lett.98,096805(2007)[18]Hofheinz,M.et al.,Individual charge traps in siliconnanowires,Eur.Phys.J.B54,299307(2006)[19]Pierre,M.,Hofheinz,M.,Jehl,X.,Sanquer,M.,Molas,G.,Vinet,M.,Deleonibus S.,Oﬀset charges acting as ex-cited states in quantum dots spectroscopy,Eur.Phys.J.B70,475-481(2009)[20]Goldhaber-Gordon,D.,Gres,J.,Kastner,M.A.,Shtrik-man,H.,Mahalu, D.,Meirav,U.,From the Kondo Regime to the Mixed-Valence Regime in a Single-Electron Transistor,Phys.Rev.Lett.81,5225(1998) [21]Although the value of s=0.22stems from SU(2)spinKondo processes,it is valid for SU(4)-Kondo systems as well[8,25].[22]Paaske,J.,Rosch,A.,W¨o lﬂe,P.,Mason,N.,Marcus,C.M.,Nyg˙ard,Non-equilibrium singlet-triplet Kondo ef-fect in carbon nanotubes,Nature Physics2,460(2006) [23]Osorio, E.A.et al.,Electronic Excitations of a SingleMolecule Contacted in a Three-Terminal Conﬁguration, Nanoletters7,3336-3342(2007)[24]Meir,Y.,Wingreen,N.S.,Lee,P.A.,Low-TemperatureTransport Through a Quantum Dot:The Anderson Model Out of Equilibrium,Phys.Rev.Lett.70,2601 (1993)[25]Lim,J.S.,Choi,M-S,Choi,M.Y.,L´o pez,R.,Aguado,R.,Kondo eﬀects in carbon nanotubes:From SU(4)to SU(2)symmetry,Phys.Rev.B74,205119(2006) [26]Hada,Y.,Eto,M.,Electronic states in silicon quan-tum dots:Multivalley artiﬁcial atoms,Phys.Rev.B68, 155322(2003)[27]Eto,M.,Hada,Y.,Kondo Eﬀect in Silicon QuantumDots with Valley Degeneracy,AIP Conf.Proc.850,1382-1383(2006)[28]A comparable process in the direct transport throughSi/SiGe double dots(Lifetime Enhanced Transport)has been recently proposed[29].[29]Shaji,N.et.al.,Spin blockade and lifetime-enhancedtransport in a few-electron Si/SiGe double quantum dot, Nature Physics4,540(2008)7Supporting InformationFinFET DevicesThe FinFETs used in this study consist of a silicon nanowire connected to large contacts etched in a60nm layer of p-type Silicon On Insulator.The wire is covered with a nitrided oxide(1.4nm equivalent SiO2thickness) and a narrow poly-crystalline silicon wire is deposited perpendicularly on top to form a gate on three faces.Ion implantation over the entire surface forms n-type degen-erate source,drain,and gate electrodes while the channel protected by the gate remains p-type,see Fig.1a of the main article.The conventional operation of this n-p-n ﬁeld eﬀect transistor is to apply a positive gate voltage to create an inversion in the channel and allow a current toﬂow.Unintentionally,there are As donors present be-low the Si/SiO2interface that show up in the transport characteristics[1].Relation between∆and T KThe information obtained on T K in the main article allows us to investigate the relation between the splitting (∆)of the ground(E GS)-andﬁrst excited(E1)-state and T K.It is expected that T K decreases as∆increases, since a high∆freezes out valley-stateﬂuctuations.The relationship between T K of an SU(4)system and∆was calculated by Eto[2]in a poor mans scaling approach ask B T K(∆) B K =k B T K(∆=0)ϕ(2)whereϕ=ΓE1/ΓGS,withΓE1andΓGS the lifetimes of E1and E GS respectively.Due to the small∆com-pared to the barrier height between the atom and the source/drain contact,we expectϕ∼1.Together with ∆=1meV and T K∼2.7K(for sample H67)and∆=2meV and T K∼6K(for sample J17),Eq.2yields k B T K(∆)/k B T K(∆=0)=0.4and k B T K(∆)/k B T K(∆= 0)=0.3respectively.We can thus conclude that the rela-tively high∆,which separates E GS and E1well in energy, will certainly quench valley-stateﬂuctuations to a certain degree but is not expected to reduce T K to a level that Valley eﬀects become obscured.Valley Kondo density of statesHere,we explain in some more detail the relation be-tween the density of states induced by the Kondo eﬀects and the resulting current.The Kondo density of states (DOS)has three main peaks,see Fig.1a.A central peak at E F=0due to processes without valley-stateﬂip and two peaks at E F=±∆due to processes with valley-state ﬂip,as explained in the main text.Even a small asym-metry(ϕclose to1)will split the Valley Kondo DOS into an SU(2)-and an SU(4)-part[3],indicated in Fig1b in black and red respectively.The SU(2)-part is positioned at E F=0or E F=±∆,while the SU(4)-part will be shifted to slightly higher positive energy(on the order of T K).A voltage bias applied between the source and FIG.1:(a)dI SD/dV SD as a function of V SD in the Kondo regime(at395mV G)of sample J17.The substructure in the Kondo resonances is the result of a small diﬀerence between ΓE1andΓGS.This splits the peaks into a(central)SU(2)-part (black arrows)and two SU(4)-peaks(red arrows).(b)Density of states in the channel as a result ofϕ(=ΓE1/ΓGS)<1and applied V SD.drain leads results in the Kondo peaks to split,leaving a copy of the original structure in the DOS now at the E F of each lead,which is schematically indicated in Fig.1b by a separate DOS associated with each contact.The current density depends directly on the density of states present within the bias window deﬁned by source/drain (indicated by the gray area in Fig1b)[4].The splitting between SU(2)-and SU(4)-processes will thus lead to a three-peak structure as a function of V SD.Figure.1a has a few more noteworthy features.The zero-bias resonance is not positioned exactly at V SD=0, as can also be observed in the transport data(Fig1c of the main article)where it is a few hundredµeV above the Fermi energy near the D0charge state and a few hundredµeV below the Fermi energy near the D−charge state.This feature is also known to arise in the Kondo strong coupling limit[5,6].We further observe that the resonances at V SD=+/-2mV diﬀer substantially in magnitude.This asymmetry between the two side-peaks can actually be expected from SU(4)Kondo sys-tems where∆is of the same order as(but of course al-ways smaller than)the energy spacing between E GS and。

友谊的甘霖浇灌我心田：温情故事分享

友谊的甘霖浇灌我心田：温情故事分享In the tapestry of life, friendships are the golden threads that weave a tapestry of shared experiences, laughter, and solace. They are the silent symphony that harmonizes our souls, and the gentle rain that滋润我们的心田. Today, I would like to share a poignant story that exemplifies the profound impact of true friendship.Once upon a time, in a bustling city, there were two young friends named Lily and Rose. Their paths crossed at a university where they pursued their dreams, each with their unique strengths and passions. Lily was a reserved intellectual, captivated by the mysteries of the universe, while Rose was an effervescent optimist, whose infectious smile could light up any room.Their friendship blossomed over countless cups of coffee,late-night study sessions, and shared dreams. The first time they embarked on a long walk together, they found themselves discussing everything from quantum physics to the intricacies of human emotions. It was during these walks that they discovered their capacity for empathy and understanding, forming a bond that transcended academic boundaries.One winter, disaster struck when Lily fell ill with a severe flu. She was bedridden and unable to attend classes or even meet her dear friend. Rose, undeterred, became a beacon of warmth. She cooked Lily's favorite meals, delivered them to her bedside, and read her assignments aloud. Her unwavering presence and relentless support were a testament to the depth of their friendship.As the days turned into weeks, Lily slowly recovered, but the memory of Rose's selflessness remained etched in her heart. She realized that it was not just the physical care that nourished her, but the emotional support and understanding that truly made her feel cared for. This simple act of kindness,浇灌在她心灵的土壤中，成为友谊的甘霖。

等离子体环境中Kerr黑洞的暗影

上海师范大学硕士学位论文摘要摘　要自从广义相对论诞生以来，黑洞作为它的一个重要结论，一直是理论研究的一个热门对象。

长期以来人们从各个不同的角度对黑洞的性质进行了广泛而深入的讨论。

本文的研究内容是通过黑洞对光线的影响得到的观测结果即黑洞暗影，反向推出黑洞的性质参数。

随着事件视界望远镜项目(EHT)的进行，黑洞暗影的研究在最近几年掀起了又一波高潮。

我们通过一系列的调研，掌握了两种计算黑洞暗影的方法，即Hamilton-Jacobi方法和反向射线追踪法。

我们首先用Hamilton-Jacobi 方法计算了真空环境下的Kerr黑洞暗影的大小和形状，从得到的结果看出影响黑洞暗影的主要因素为黑洞的质量M和自旋a；然后用反向射线追踪法对等离子体环境中的Kerr黑洞进行了研究，并引入两个参数，即黑洞暗影半径R s和形变参数σ对黑洞暗影的形状进行描述。

我们看到通过增加黑洞的自旋参数，黑洞暗影的图像会发生改变，变得更加不规则。

在等离子体环境下，黑洞暗影的形状会因受到等离子体的影响而发生变化。

跟在真空环境下不同，等离子体环境下的黑洞暗影，其形状和大小都跟光子的频率相关，即在不同波段上观测到的黑洞暗影大小和形状都不同。

黑洞暗影进行深入研究不仅可以用来检验广义相对论，而且还可以通过对黑洞暗影的形状和大小的分析，得到黑洞周围的时空性质。

关键词：Hamilton-Jacobi方法，反向射线追踪法，黑洞暗影，等离子体Abstract Shanghai Normal University Master of PhilosophyAbstractBlack hole is one of the most popular object in theoretical study,since the general theory of relaticity was born.A lot of researchers studied the properties of block hole from different aspects in history.Of course a black hole itself cannot be seen directly but if it is in front of a luminous background or more generally,in the centre of a luminous asymptotically flat region(because of the bending of light it need not be behind the hole!)—it will cast a specific shadow.With the advance of the Event Horizon Telescope(EHT) project,the study of black hole shadow has stimulate a stirring of interest again.To study the shadow of black hole:,two methods usually be used:one is analytical,which use the Hamilton-Jacobi formalism of null geodesic;Another is numerical and a ray racing algorithm is applied.At first we use Hamilton-Jacobi Equation to research the shadow of Kerr black hole in vacuum environment,the size and the shape of the shadow depend on the mass and the angular momentum,and they can also depend on other parameters specific of the particular model adopted.Then we investigate the shadow of Kerr black hole with plasma by Ray-Tracing Algorithm.We discover that shape and size of shadow will effected by properties of plasma.The study of black hole shadow can not only used to explore the property of space-time in the vicinity of a black hole,but also to test the general theory of relativity.Keywords:the Hamilton-Jacobi formalism,Ray Tracing Algorithm,black hole shadow, plasma.目录第一章绪论 (1)1.1研究工作的背景与意义 (1)1.2黑洞暗影的国内外研究历史与现状 (2)1.3本文的主要贡献与创新 (3)1.4本论文的结构安排 (3)第二章黑洞基础简介 (4)2.1黑洞 (4)2.2Kerr黑洞 (5)第三章计算Kerr黑洞暗影：Hamilton-Jacobi方法 (6)3.1Hamilton-Jacobi方程 (6)3.2运动方程 (8)3.2.1Null测地线 (9)3.2.2光子的球形轨道 (9)3.3天球坐标 (9)3.4Kerr黑洞的暗影呈现 (12)第四章反向射线追溯法 (13)4.1在被等离子体包围的黑洞附近的光线 (13)4.2光线在等离子体的中的传播 (13)4.2.1应用到轴对称时空 (14)4.2.2观察者平面 (16)4.2.3初始条件 (17)4.3数值计算的结果 (18)4.3.1等离子体环境中Kerr黑洞暗影的刻画 (18)4.3.2等离子体对黑洞暗影影响的量化 (20)4.3.3黑洞暗影的四色渲染图 (21)第五章全文总结与展望 (23)5.1全文总结 (23)5.2后续工作展望 (23)参考文献 (24)攻读学位期间取得的研究成果 (28)致谢 (29)上海师范大学硕士学位论文第一章绪论第一章绪论1.1研究工作的背景与意义经过对太阳系和宇宙中各种现象的观测，广义相对论已经得到了很好的验证。

安倍晋三美国国会演讲英文全文

安倍晋三美国国会演讲英文全文2015年9月8日，日本自民党总裁选举公示，现任总裁安倍晋三是唯一候选人，“无投票”连任，任期3年。

以下是店铺整理了安倍晋三美国国会演讲英文全文，供你参考。

安倍晋三美国国会演讲英文全文如下：Toward an Alliance of HopeMr. Speaker, Mr. Vice President, distinguished members of the Senate and the House, distinguished guests, ladies and gentlemen,Back in June, 1957, Nobusuke Kishi, my grandfather, standing right here, as Prime Minister of Japan, began his address, by saying, and I quote,"It is because of our strong belief in democratic principles and ideals that Japan associates her self with the free nations of the world."58 years have passed. Today, I am honored to stand here as the first Japanese Prime Minister ever to address your joint meeting. I extend my heartfelt gratitude to you for inviting me.I have lots of things to tell you. But I am here with no ability, nor the intention, to filibuster.As I stand in front of you today, the names of your distinguished colleagues that Japan welcomed as your ambassadors come back to me: the honorable Mike Mansfield, Walter Mondale, T om Foley, and Howard Baker.On behalf of the Japanese people, thank you so very much for sending us such shining champions of democracy.Ambassador Caroline Kennedy also embodies the tradition of American democracy. Thank you so much, Ambassador Kennedy, for all the dynamic work you have done for all of us.We all miss Senator Daniel Inouye, who symbolized the honor and achievements of Japanese-Americans.America and ILadies and gentlemen, my first encounter with America goes back to my days as a student, when I spent a spell in California.A lady named Catherine Del Francia let me live in her house.She was a widow, and always spoke of her late husband saying, "You know, he was much more handsome than Gary Cooper." She meant it. She really did.In the gallery, you see, my wife, Akie, is there. I don't dare ask what she says about me.Mrs. Del Francia's Italian cooking was simply out of this world. She was cheerful, and so kind, as to let lots and lots of people stop by at her house.They were so diverse. I was amazed and said to myself, "America is an awesome country."Later, I took a job at a steelmaker, and I was given the chance to work in New York.Here in the U.S. rank and hierarchy are neither here nor there. People advance based on merit. When you discuss things you don't pay much attention to who is junior or senior. You just choose the best idea, no matter who the idea was from.This culture intoxicated me.So much so, after I got elected as a member of the House, some of the old guard in my party would say, "hey, you're so cheeky, Abe."American Democracy and JapanAs for my family name, it is not "Eighb."Some Americans do call me that every now and then, but I don't take offense.That's because, ladies and gentlemen, the Japanese, ever since they started modernization, have seen the very foundation for democracy in that famous line in the Gettysburg Address.The son of a farmer-carpenter can become the President The fact that such a country existed woke up the Japanese of the late 19th century to democracy.For Japan, our encounter with America was also our encounter with democracy. And that was more than 150 years ago, giving us a mature history together.World War II MemorialBefore coming over here, I was at the World War II Memorial. It was a place of peace and calm that struck me as a sanctuary. The air was filled with the sound of water breaking in the fountains.In one corner stands the Freedom Wall. More than 4,000 gold stars shine on the wall.I gasped with surprise to hear that each star represents the lives of 100 fallen soldiers.I believe those gold stars are a proud symbol of the sacrifices in defending freedom. But in those gold stars, we also find the pain, sorrow, and love for family of young Americans who otherwise would have lived happy lives.Pearl Harbor, Bataan Corregidor, Coral Sea. The battles engraved at the Memorial crossed my mind, and I reflected upon the lost dreams and lost futures of those young Americans.History is harsh. What is done cannot be undone.With deep repentance in my heart, I stood there in silent prayers for some time.My dear friends, on behalf of Japan and the Japanese people, I offer with profound respect my eternal condolences to the soulsof all American people that were lost during World War II.Late Enemy, Present FriendLadies and gentlemen, in the gallery today is Lt. Gen. Lawrence Snowden.Seventy years ago in February, he landed on Ioto, or the island of Iwo Jima, as a captain in command of a company. In recent years, General Snowden has often participated in the memorial services held jointly by Japan and the U.S. on Ioto.He said, and I quote, "We didn't and don't go to Iwo Jima to celebrate victory, but for the solemn purpose to pay tribute to and honor those who lost their lives on both sides."Next to General Snowden sits Diet Member Yoshitaka Shindo, who is a former member of my Cabinet. His grandfather, General Tadamichi Kuribayashi, whose valor we remember even today, was the commander of the Japanese garrison during the Battle of Iwo Jima.What should we call this, if not a miracle of history?Enemies that had fought each other so fiercely have become friends bonded in spirit.To General Snowden, I say that I pay tribute to your efforts for reconciliation. Thank you so very much.America and Post-War JapanPost war, we started out on our path bearing in mind feelings of deep remorse over the war. Our actions brought suffering to the peoples in Asian countries. We must not avert our eyes from that. I will uphold the views expressed by the previous prime ministers in this regard.We must all the more contribute in every respect to the development of Asia. We must spare no effort in working for the peace and prosperity of the region.Reminding ourselves of all that, we have come all this way. I am proud of this path we have taken.70 years ago, Japan had been reduced to ashes.Then came each and every month from the citizens of the United States gifts to Japan like milk for our children and warm sweaters, and even goats. Yes, from America, 2,036 goats came to Japan.And it was Japan that received the biggest benefit from the very beginning by the post-war economic system that the U.S. had fostered by opening up its own market and calling for a liberal world economy.Later on, from the 1980's, we saw the rise of the Republic of Korea, Taiwan, the ASEAN countries, and before long, China as well.This time, Japan too devotedly poured in capital and technologies to support their growths.Meanwhile in the U.S., Japan created more employment than any other foreign nation but one, coming second only to the U.K.TPPIn this way, prosperity was fostered first by the U.S., and second by Japan. And prosperity is nothing less than the seedbed for peace.Involving countries in Asia-Pacific whose backgrounds vary, the U.S. and Japan must take the lead. We must take the lead to build a marketthat is fair, dynamic, sustainable, and is also free from the arbitrary intentions of any nation.In the Pacific market, we cannot overlook sweat shops or burdens on the environment. Nor can we simply allow free riders on intellectualproperty.No. Instead, we can spread our shared values around the world and have them take root: the rule of law, democracy, and freedom.That is exactly what the TPP is all about.Furthermore, the TPP goes far beyond just economic benefits. It is also about our security. Long-term, its strategic value is awesome. We should never forget that.The TPP covers an area that accounts for 40 per cent of the world economy, and one third of global trade. We must turn the area into a region for lasting peace and prosperity.That is for the sake of our children and our children's children. As for U.S.-Japan negotiations, the goal is near. Let us bring the TPP to a successful conclusion through our joint leadership.Reforms for a Stronger JapanAs a matter of fact, I have something I can tell you now.It was about 20 years ago. The GATT negotiations for agriculture were going on.I was much younger, and like a ball of fire, and opposed to opening Japan's agricultural market. I even joined farmers' representatives in a rally in front of the Parliament.However, Japan's agriculture has gone into decline over these last 20 years. The average age of our farmers has gone up by 10 years and is now more than 66 years old.Japan's agriculture is at a crossroads. In order for it to survive, it has to change now.We are bringing great reforms toward the agriculture policy that's been in place for decades. We are also bringing sweeping reforms to our agricultural cooperatives that have not changed in 60 long years.Corporate governance in Japan is now fully in line with global standards, because we made it stronger.Rock-solid regulations are being broken in such sectors as medicine and energy. And I am the spearhead.To turn around our depopulation, I am determined to do whatever it takes. We are changing some of our old habits to empower women so they can get more actively engaged in all walks of life.In short, Japan is right in the middle of a quantum leap.My dear members of the Congress, please do come and see the new Japan, where we have regained our spirit of reform and our sense of speed.Japan will not run away from any reforms. We keep our eyes only on the road ahead and push forward with structural reforms.That's TINA: There Is No Alternative. And there is no doubt about it whatsoever.Post War Peace and Japan's ChoiceMy dear colleagues, the peace and security of the post-war world was not possible without American leadership.Looking back, it makes me happy all the time that Japan of years past made the right decision.As I told you at the outset, citing my grandfather, that decision was to choose a path.That's the path for Japan to ally itself with the U.S., and to go forward as a member of the Western world.In the end, together with the U.S. and other like-minded democracies, we won the Cold War.That's the path that made Japan grow and prosper. And even today, there is no alternative.The Alliance: its Mission for the RegionMy dear colleagues, we support the "rebalancing" by the U.S. in order to enhance the peace and security of the Asia-Pacific region.And I will state clearly. We will support the U.S. effort first, last, and throughout.Japan has deepened its strategic relations with Australia and India. We are enhancing our cooperation across many fields with the countries of ASEAN and the Republic of Korea.Adding those partners to the central pillar that is the U.S.-Japan alliance, our region will get stable remarkably more.Now, Japan will provide up to 2.8 billion dollars in assistance to help improve U.S. bases in Guam, which will gain strategic significance even more in the future.As regards the state of Asian waters, let me underscore here my three principles.First, states shall make their claims based on international law.Second, they shall not use force or coercion to drive their claims.And third, to settle disputes, any disputes, they shall do so by peaceful means.We must make the vast seas stretching from the Pacific to the Indian Oceans seas of peace and freedom, where all follow the rule of law.For that very reason we must fortify the U.S.-Japan alliance. That is our responsibility.Now, let me tell you.In Japan we are working hard to enhance the legislative foundations for our security.Once in place, Japan will be much more able to provide a seamless response for all levels of crisis.These enhanced legislative foundations should make the cooperation between the U.S. military and Japan's Self Defense Forces even stronger, and the alliance still more solid, providing credible deterrence for the peace in the region.This reform is the first of its kind and a sweeping one in our post-war history. We will achieve this by this coming summer.Now, I have something to share with you.The day before yesterday Secretaries Kerry and Carter met our Foreign Minister Kishida and Defense Minister Nakatani for consultations.As a result, we now have a new framework. A framework to better put together the forces of the U.S. and Japan.A framework that is in line with the legislative attempts going on in Japan.That is what's necessary to build peace, more reliable peace in the region. And that is namely the new Defense Cooperation Guidelines.Yesterday, President Obama and I fully agreed on the significance of these Guidelines.Ladies and gentlemen, we agreed on a document that is historic.Japan's New BannerIn the early 1990s, in the Persian Gulf Japan's Self-Defense Forces swept away sea mines.For 10 years in the Indian Ocean, Japanese Self-Defense Forces supported your operation to stop the flow of terrorists and arms.Meanwhile in Cambodia, the Golan Heights, Iraq, Haiti, and South Sudan, members of our Self-Defense Forces provided humanitarian support and peace keeping operations. Theirnumber amounts to 50,000.Based on this track record, we are resolved to take yet more responsibility for the peace and stability in the world.It is for that purpose we are determined to enact all necessary bills by this coming summer. And we will do exactly that.We must make sure human security will be preserved in addition to national security. That's our belief, firm and solid.We must do our best so that every individual gets education, medical support, and an opportunity to rise to be self-reliant.Armed conflicts have always made women suffer the most. In our age, we must realize the kind of world where finally women are free from human rights abuses.Our servicemen and women have made substantial accomplishments. So have our aid workers who have worked so steadily.Their combined sum has given us a new self-identity.That's why we now hold up high a new banner that is "proactive contribution to peace based on the principle of international cooperation."Let me repeat. "Proactive contribution to peace based on the principle of international cooperation" should lead Japan along its road for the future.Problems we face include terrorism, infectious diseases, natural disasters and climate change.The time has come for the U.S.-Japan alliance to face up to and jointly tackle those challenges that are new.After all our alliance has lasted more than a quarter of the entire history of the United States.It is an alliance that is sturdy, bound in trust and friendship,deep between us.No new concept should ever be necessary for the alliance that connects us, the biggest and the second biggest democratic powers in the free world, in working together.Always, it is an alliance that cherishes our shared values of the rule of law, respect for human rights and freedom.Hope for the futureWhen I was young in high school and listened to the radio, there was a song that flew out and shook my heart.It was a song by Carol King."When you're down and troubled, close your eyes and think of me, and I'll be there to brighten up even your darkest night."And that day, March 11, 2011, a big quake, a tsunami, and a nuclear accident hit the northeastern part of Japan.The darkest night fell upon Japan.But it was then we saw the U.S. armed forces rushing to Japan to the rescue at a scale never seen or heard before.Lots and lots of people from all corners of the U.S. extended the hand of assistance to the children in the disaster areas.Yes, we've got a friend in you.Together with the victims you shed tears. You gave us something, something very, very precious.That was hope, hope for the future.Ladies and gentlemen, the finest asset the U.S. has to give to the world was hope, is hope, will be, and must always be hope.Distinguished representatives of the citizens of the United States, let us call the U.S.-Japan alliance, an alliance of hope.Let the two of us, America and Japan, join our hands together and do our best to make the world a better, a much better, place to live.Alliance of hope . Together, we can make a difference.Thank you so much.安倍晋三人物评价：日本媒体称安倍晋三是“小泉的正统接班人”。

振动力学专业英语及词汇

振动力学专业英语及词汇振动方面的专业英语及词汇振动方面的专业英语及词汇参见《工程振动名词术语》1 振动信号的时域、频域描述振动过程 (Vibration Process)简谐振动 (Harmonic Vibration)周期振动 (Periodic Vibration)准周期振动 (Ouasi-periodic Vibration)瞬态过程 (Transient Process)随机振动过程 (Random Vibration Process)各态历经过程 (Ergodic Process)确定性过程 (Deterministic Process)振幅 (Amplitude)相位 (Phase)初相位 (Initial Phase)频率 (Frequency)角频率 (Angular Frequency)周期 (Period)复数振动 (Complex Vibration)复数振幅 (Complex Amplitude)峰值 (Peak-value)平均绝对值 (Average Absolute Value)有效值 (Effective Value，RMS Value)均值 (Mean Value，Average Value)傅里叶级数 (FS，Fourier Series)傅里叶变换 (FT，Fourier Transform)傅里叶逆变换 (IFT，Inverse Fourier Transform)离散谱 (Discrete Spectrum)连续谱 (Continuous Spectrum)傅里叶谱 (Fourier Spectrum)线性谱 (Linear Spectrum)幅值谱 (Amplitude Spectrum)相位谱 (Phase Spectrum)均方值 (Mean Square Value)方差 (Variance)协方差 (Covariance)自协方差函数 (Auto-covariance Function)互协方差函数 (Cross-covariance Function)自相关函数 (Auto-correlation Function)互相关函数 (Cross-correlation Function)标准偏差 (Standard Deviation)相对标准偏差 (Relative Standard Deviation)概率 (Probability)概率分布 (Probability Distribution)高斯概率分布(Gaussian Probability Distribution) 概率密度(Probability Density)集合平均 (Ensemble Average)时间平均 (Time Average)功率谱密度 (PSD，Power Spectrum Density)自功率谱密度 (Auto-spectral Density)互功率谱密度 (Cross-spectral Density)均方根谱密度 (RMS Spectral Density)能量谱密度 (ESD，Energy Spectrum Density)相干函数 (Coherence Function)帕斯瓦尔定理 (Parseval''''s Theorem)维纳，辛钦公式 (Wiener-Khinchin Formula2 振动系统的固有特性、激励与响应振动系统 (Vibration System)激励 (Excitation)响应 (Response)单自由度系统 (Single Degree-Of-Freedom System) 多自由度系统(Multi-Degree-Of- Freedom System) 离散化系统(Discrete System)连续体系统 (Continuous System)刚度系数 (Stiffness Coefficient)自由振动 (Free Vibration)自由响应 (Free Response)强迫振动 (Forced Vibration)强迫响应 (Forced Response)初始条件 (Initial Condition)固有频率 (Natural Frequency)阻尼比 (Damping Ratio)衰减指数 (Damping Exponent)阻尼固有频率 (Damped Natural Frequency)对数减幅系数 (Logarithmic Decrement)主频率 (Principal Frequency)无阻尼模态频率 (Undamped Modal Frequency)模态 (Mode)主振动 (Principal Vibration)振型 (Mode Shape)振型矢量 (Vector Of Mode Shape)模态矢量 (Modal Vector)正交性 (Orthogonality)展开定理 (Expansion Theorem)主质量 (Principal Mass)模态质量 (Modal Mass)主刚度 (Principal Stiffness)模态刚度 (Modal Stiffness)正则化 (Normalization)振型矩阵 (Matrix Of Modal Shape)模态矩阵 (Modal Matrix)主坐标 (Principal Coordinates)模态坐标 (Modal Coordinates)模态分析 (Modal Analysis)模态阻尼比 (Modal Damping Ratio)频响函数 (Frequency Response Function)幅频特性 (Amplitude-frequency Characteristics)相频特性 (Phase frequency Characteristics)共振 (Resonance)半功率点 (Half power Points)波德图(Bodé Plot)动力放大系数 (Dynamical Magnification Factor)单位脉冲 (Unit Impulse)冲激响应函数 (Impulse Response Function)杜哈美积分(Duhamel’s Integral)卷积积分 (Convolution Integral)卷积定理 (Convolution Theorem)特征矩阵 (Characteristic Matrix)阻抗矩阵 (Impedance Matrix)频响函数矩阵 (Matrix Of Frequency Response Function) 导纳矩阵 (Mobility Matrix)冲击响应谱 (Shock Response Spectrum)冲击激励 (Shock Excitation)冲击响应 (Shock Response)冲击初始响应谱 (Initial Shock Response Spectrum) 冲击剩余响应谱(Residual Shock Response Spectrum) 冲击最大响应谱(Maximum Shock Response Spectrum) 冲击响应谱分析(Shock Response Spectrum Analysis 3 模态试验分析模态试验 (Modal Testing)机械阻抗 (Mechanical Impedance)位移阻抗 (Displacement Impedance)速度阻抗 (Velocity Impedance)加速度阻抗 (Acceleration Impedance)机械导纳 (Mechanical Mobility)位移导纳 (Displacement Mobility)速度导纳 (Velocity Mobility)加速度导纳 (Acceleration Mobility)驱动点导纳 (Driving Point Mobility)跨点导纳 (Cross Mobility)传递函数 (Transfer Function)拉普拉斯变换 (Laplace Transform)传递函数矩阵 (Matrix Of Transfer Function)频响函数 (FRF，Frequency Response Function)频响函数矩阵 (Matrix Of FRF)实模态 (Normal Mode)复模态 (Complex Mode)模态参数 (Modal Parameter)模态频率 (Modal Frequency)模态阻尼比 (Modal Damping Ratio)模态振型 (Modal Shape)模态质量 (Modal Mass)模态刚度 (Modal Stiffness)模态阻力系数 (Modal Damping Coefficient)模态阻抗 (Modal Impedance)模态导纳 (Modal Mobility)模态损耗因子 (Modal Loss Factor)比例粘性阻尼 (Proportional Viscous Damping)非比例粘性阻尼 (Non-proportional Viscous Damping) 结构阻尼(Structural Damping，Hysteretic Damping) 复频率(ComplexFrequency)复振型 (Complex Modal Shape)留数 (Residue)极点 (Pole)零点 (Zero)复留数 (Complex Residue)随机激励 (Random Excitation)伪随机激励 (Pseudo Random Excitation)猝发随机激励 (Burst Random Excitation)稳态正弦激励 (Steady State Sine Excitation)正弦扫描激励 (Sweeping Sine Excitation)锤击激励 (Impact Excitation)频响函数的H1 估计 (FRF Estimate by H1)频响函数的H2 估计 (FRF Estimate by H2)频响函数的H3 估计 (FRF Estimate by H3)单模态曲线拟合法 (Single-mode Curve Fitting Method)多模态曲线拟合法 (Multi-mode Curve Fitting Method)模态圆 (Mode Circle)剩余模态 (Residual Mode)幅频峰值法 (Peak Value Method)实频-虚频峰值法 (Peak Real／Imaginary Method)圆拟合法 (Circle Fitting Method)加权最小二乘拟合法 (Weighting Least Squares Fitting method) 复指数拟合法 (Complex Exponential Fitting method)1.2 振动测试的名词术语1 传感器测量系统传感器测量系统 (Transducer Measuring System)传感器 (Transducer)振动传感器 (Vibration Transducer)机械接收 (Mechanical Reception)机电变换 (Electro-mechanical Conversion)测量电路 (Measuring Circuit)惯性式传感器 (Inertial Transducer，Seismic Transducer) 相对式传感器 (Relative Transducer)电感式传感器 (Inductive Transducer)应变式传感器 (Strain Gauge Transducer)电动力传感器 (Electro-dynamic Transducer)压电式传感器 (Piezoelectric Transducer)压阻式传感器 (Piezoresistive Transducer)电涡流式传感器 (Eddy Current Transducer)伺服式传感器 (Servo Transducer)灵敏度 (Sensitivity)复数灵敏度 (Complex Sensitivity)分辨率 (Resolution)频率范围 (Frequency Range)线性范围 (Linear Range)频率上限 (Upper Limit Frequency)频率下限 (Lower Limit Frequency)静态响应 (Static Response)零频率响应 (Zero Frequency Response)动态范围 (Dynamic Range)幅值上限 Upper Limit Amplitude)幅值下限 (Lower Limit Amplitude)最大可测振级 (Max．Detectable Vibration Level)最小可测振级 (Min．Detectable Vibration Level)信噪比 (S/N Ratio)振动诺模图 (Vibration Nomogram)相移 (Phase Shift)波形畸变 (Wave-shape Distortion)比例相移 (Proportional Phase Shift)惯性传感器的稳态响应(Steady Response Of Inertial Transducer)惯性传感器的稳击响应 (Shock Response Of Inertial Transducer) 位移计型的频响特性(Frequency Response Characteristics Vibrometer)加速度计型的频响特性(Frequency Response Characteristics Accelerometer) 幅频特性曲线 (Amplitude-frequency Curve) 相频特性曲线 (Phase-frequency Curve)固定安装共振频率 (Mounted Resonance Frequency)安装刚度 (Mounted Stiffness)有限高频效应 (Effect Of Limited High Frequency)有限低频效应 (Effect Of Limited Low Frequency)电动式变换 (Electro-dynamic Conversion)磁感应强度 (Magnetic Induction， Magnetic Flux Density)磁通 (Magnetic Flux)磁隙 (Magnetic Gap)电磁力 (Electro-magnetic Force)相对式速度传 (Relative Velocity Transducer)惯性式速度传感器 (Inertial Velocity Transducer)速度灵敏度 (Velocity Sensitivity)电涡流阻尼 (Eddy-current Damping)无源微(积)分电路 (Passive Differential (Integrate) Circuit) 有源微(积)分电路(Active Differential (Integrate) Circuit) 运算放大器(Operational Amplifier)时间常数 (Time Constant)比例运算 (Scaling)积分运算 (Integration)微分运算 (Differentiation)高通滤波电路 (High-pass Filter Circuit)低通滤波电路 (Low-pass Filter Circuit)截止频率 (Cut-off Frequency)压电效应 (Piezoelectric Effect)压电陶瓷 (Piezoelectric Ceramic)压电常数 (Piezoelectric Constant)极化 (Polarization)压电式加速度传感器 (Piezoelectric Acceleration Transducer) 中心压缩式 (Center Compression Accelerometer)三角剪切式 (Delta Shear Accelerometer)压电方程 (Piezoelectric Equation)压电石英 (Piezoelectric Quartz)电荷等效电路 (Charge Equivalent Circuit)电压等效电路 (Voltage Equivalent Circuit)电荷灵敏度 (Charge Sensitivity)电压灵敏度 (Voltage Sensitivity)电荷放大器 (Charge Amplifier)适调放大环节 (Conditional Amplifier Section)归一化 (Uniformization)电荷放大器增益 (Gain Of Charge Amplifier)测量系统灵敏度 (Sensitivity Of Measuring System)底部应变灵敏度 (Base Strain Sensitivity)横向灵敏度 (Transverse Sensitivity)地回路 (Ground Loop)力传感器 (Force Transducer)力传感器灵敏度 (Sensitivity Of Force Transducer)电涡流 (Eddy Current)前置器 (Proximitor)间隙-电压曲线 (Voltage vs Gap Curve)间隙-电压灵敏度 (Voltage vs Gap Sensitivity)压阻效应 (Piezoresistive Effect)轴向压阻系数 (Axial Piezoresistive Coefficient)横向压阻系数 (Transverse Piezoresistive Coefficient)压阻常数 (Piezoresistive Constant)单晶硅 (Monocrystalline Silicon)应变灵敏度 (Strain Sensitivity)固态压阻式加速度传感器(Solid State Piezoresistive Accelerometer) 体型压阻式加速度传感器 (Bulk Type Piezoresistive Accelerometer) 力平衡式传感器 (Force Balance Transducer) 电动力常数 (Electro-dynamic Constant)机电耦合系统 (Electro-mechanical Coupling System)2 检测仪表、激励设备及校准装置时间基准信号 (Time Base Signal)李萨茹图 (Lissojous Curve)数字频率计 (Digital Frequency Meter)便携式测振表 (Portable Vibrometer)有效值电压表 (RMS Value Voltmeter)峰值电压表 (Peak-value Voltmeter)平均绝对值检波电路 (Average Absolute Value Detector)峰值检波电路 (Peak-value Detector)准有效值检波电路 (Quasi RMS Value Detector)真有效值检波电路 (True RMS Value Detector)直流数字电压表 (DVM，DC Digital Voltmeter)数字式测振表 (Digital Vibrometer)A/D 转换器 (A/D Converter)D/A 转换器 (D/A Converter)相位计 (Phase Meter)电子记录仪 (Lever Recorder)光线示波器 (Oscillograph)振子 (Galvonometer)磁带记录仪 (Magnetic Tape Recorder)DR 方式(直接记录式) (Direct Recorder)FM 方式(频率调制式) (Frequency Modulation)失真度 (Distortion)机械式激振器 (Mechanical Exciter)机械式振动台 (Mechanical Shaker)离心式激振器 (Centrifugal Exciter)电动力式振动台 (Electro-dynamic Shaker)电动力式激振器 (Electro-dynamic Exciter)液压式振动台 (Hydraulic Shaker)液压式激振器 (Hydraulic Exciter)电液放大器 (Electro-hydraulic Amplifier)磁吸式激振器 (Magnetic Pulling Exciter)涡流式激振器 (Eddy Current Exciter)压电激振片 (Piezoelectric Exciting Elements)冲击力锤 (Impact Hammer)冲击试验台 (Shock Testing Machine)激振控制技术 (Excitation Control Technique)波形再现 (Wave Reproduction)压缩技术 (Compression Technique)均衡技术 (Equalization Technique)交越频率 (Crossover Frequency)综合技术 (Synthesis Technique)校准 (Calibration)分部校准 (Calibration for Components in system) 系统校准 (Calibration for Over-all System)模拟传感器 (Simulated Transducer)静态校准 (Static Calibration)简谐激励校准 (Harmonic Excitation Calibration) 绝对校准 (Absolute Calibration)相对校准 (Relative Calibration)比较校准 (Comparison Calibration)标准振动台 (Standard Vibration Exciter)读数显微镜法 (Microscope-streak Method)光栅板法 (Ronchi Ruling Method)光学干涉条纹计数法 (Optical Interferometer Fringe Counting Method)光学干涉条纹消失法(Optical Interferometer Fringe Disappearance Method) 背靠背安装 (Back-to-back Mounting) 互易校准法 (Reciprocity Calibration)共振梁 (Resonant Bar)冲击校准 (Impact Exciting Calibration)摆锤冲击校准 (Ballistic Pendulum Calibration)落锤冲击校准 (Drop Test Calibration)振动和冲击标准 (Vibration and Shock Standard)迈克尔逊干涉仪 (Michelson Interferometer)摩尔干涉图象 (Moire Fringe)参考传感器 (Reference Transducer)3 频率分析及数字信号处理带通滤波器 (Band-pass Filter)半功率带宽 (Half-power Bandwidth)3 dB 带宽 (3 dB Bandwidth)等效噪声带宽 (Effective Noise Bandwidth)恒带宽 (Constant Bandwidth)恒百分比带宽 (Constant Percentage Bandwidth)1/N 倍频程滤波器 (1/N Octave Filter)形状因子 (Shape Factor)截止频率 (Cut-off Frequency)中心频率 (Centre Frequency)模拟滤波器 (Analog Filter)数字滤波器 (Digital Filter)跟踪滤波器 (Tracking Filter)外差式频率分析仪 (Heterodyne Frequency Analyzer) 逐级式频率分析仪 (Stepped Frequency Analyzer)扫描式频率分析仪 (Sweeping Filter Analyzer)混频器 (Mixer)RC 平均 (RC Averaging)平均时间 (Averaging Time)扫描速度 (Sweeping Speed)滤波器响应时间 (Filter Response Time)离散傅里叶变换 (DFT，Discrete Fourier Transform) 快速傅里叶变换 (FFT，Fast Fourier Transform)抽样频率 (Sampling Frequency)抽样间隔 (Sampling Interval)抽样定理 (Sampling Theorem)抗混滤波 (Anti-aliasing Filter)泄漏 (Leakage)加窗 (Windowing)窗函数 (Window Function)截断 (Truncation)频率混淆 (Frequency Aliasing)乃奎斯特频率 (Nyquist Frequency)矩形窗 (Rectangular Window)汉宁窗 (Hanning Window)凯塞-贝塞尔窗 (Kaiser-Bessel Window)平顶窗 (Flat-top Window)平均 (Averaging)线性平均 (Linear Averaging)指数平均 (Exponential Averaging)峰值保持平均 (Peak-hold Averaging)时域平均 (Time-domain Averaging)谱平均 (Spectrum Averaging)重叠平均 (Overlap Averaging)栅栏效应 (Picket Fence Effect)吉卜斯效应 (Gibbs Effect)基带频谱分析 (Base-band Spectral Analysis)选带频谱分析 (Band Selectable Sp4ctralAnalysis)细化 (Zoom)数字移频 (Digital Frequency Shift)抽样率缩减 (Sampling Rate Reduction)功率谱估计 (Power Spectrum Estimate)相关函数估计 (Correlation Estimate)频响函数估计 (Frequency Response Function Estimate) 相干函数估计 (Coherence Function Estimate)冲激响应函数估计 (Impulse Response Function Estimate) 倒频谱 (Cepstrum)功率倒频谱 (Power Cepstrum)幅值倒频谱 (Amplitude Cepstrum)倒频率 (Quefrency)4 旋转机械的振动测试及状态监测状态监测 (Condition Monitoring)故障诊断 (Fault Diagnosis)转子 (Rotor)转手支承系统 (Rotor-Support System)振动故障 (Vibration Fault)轴振动 (Shaft Vibration)径向振动 (Radial Vibration)基频振动 (Fundamental Frequency Vibration)基频检测 (Fundamental Frequency Component Detecting) 键相信号 (Key-phase Signal)正峰相位 (+Peak Phase)高点 (High Spot)光电传感器 (Optical Transducer)同相分量 (In-phase Component)正交分量 (Quadrature Component)跟踪滤波 (Tracking Filter)波德图 (Bode Plot)极坐标图 (Polar Plot)临界转速 (Critical Speed)不平衡响应 (Unbalance Response)残余振幅 (Residual Amplitude)方位角 (Attitude Angle)轴心轨迹 (Shaft Centerline Orbit)正进动 (Forward Precession)同步正进动 (Synchronous Forward Precession)反进动 (Backward Precession)正向涡动 (Forward Whirl)反向涡动 (Backward Whirl)油膜涡动 (Oil Whirl)油膜振荡 (Oil Whip)轴心平均位置(Average Shaft Centerline Position) 复合探头(Dual Probe)振摆信号 (Runout Signal)电学振摆 (Electrical Runout)机械振摆 (Mechanical Runout)慢滚动向量 (Slow Roll Vector)振摆补偿 (Runout Compensation)故障频率特征(Frequency Characteristics Of Fault) 重力临界(Gravity Critical)对中 (Alignment)双刚度转子 (Dual Stiffness Rotor)啮合频率 (Gear-mesh Frequency)间入简谐分量 (Interharmonic Component)边带振动 (Side-band Vibration)三维频谱图 (Three Dimensional Spectral Plot)瀑布图 (Waterfall Plot)级联图 (Cascade Plot)阶次跟踪 (Order Tracking)阶次跟踪倍乘器 (Order Tracking Multiplier)监测系统 (Monitoring System)适调放大器 (Conditional Amplifier)趋势分析 (Trend Analysis)倒频谱分析 (Cepstrum Analysis) 直方图 (Histogram)确认矩阵 (Confirmation Matrix) 通频幅值 (Over-all Amplitude) 幅值谱 (Amplitude Spectrum)相位谱 (Phase Spectrum)报警限 (Alarm Level)。

3.0超高场磁共振的临床应用

IR FSE T1WI CE 3.0T
Contrast-enhanced MR Imaging 增强MRI
SPIO（超顺磁性氧化铁）对比剂：主要缩短T2*
在3.0T中，（平扫时）组织的T2*时间比 1.5T短，这种更短的T2*部分抵消了SPIO的 T2*增强效应
至今，在肝脏局灶性病变的SPIO增强检查中， SPIO增强病变与正常组织之间的对比在3.0T中并未进一步增加
3T 3D TOF-MRA flow void in the proximal portion of the right middle cerebral artery
DSA anteroposterior view a focal high-degree stenosis at the corresponding location
中枢神经系统高分辨率扫描
Propeller T2 512X512
分辨力
1.5 T
3.0 T
Figure 9a: (a, b) FLAIR images in a 22-year-old female patient with clinically isolated syndrome
1.5 T 6000/110/2000; turbo factor, 29; NEX 2; acquisition time, 3 minutes
1.5 T with 0.10 mmol/kg
3.0 T with 0.05 mmol/kg 3.0 T with 0.10 mmol/kg
Contrast-enhanced T1-weighted MR images in 46-year-old male patient with right parietal high-grade glioma

英语词汇之物理词汇

英语词汇之物理词汇英语词汇之物理词汇英语词汇-物理词汇(2)Nn-type semiconductor n型半导体NAND gate 「与非」门，「非与」门naphthalene ?natural frequency 固有频率，自然频率nature 本质near point 近点necking 颈缩negater 反相器，倒换器negative charge 负电荷negative feedback 负反馈negative ion 负离子negative supply rail 负供电轨negative terminal 负端钮，负接线柱net force 净力network 网络，网络neutral 中性，中线neutral equilibrium 中性平衡，随遇平衡neutral point 中和点neutrino 中微子neutron 中子neutron number 中子数newton 牛顿Newtons first law of motion 牛顿运动第一定律Newtons law of gravitation 牛顿万有引力定律Newtons ring 牛顿环Newtons second law of motion 牛顿运动第二定律Newtons third law of motion 牛顿运动第三定律Newtonian fluid 牛顿流体Newtonian mechanics 牛顿力学nichrome wire 镍铬线，镍铬合金线Nicol prism 尼科尔棱镜nitrogen 氮no-parallax 无视差nodal line 节线node 节点，波节noise 噪音noise level 噪音级noise pollution 噪音污染non-conservative force 非守恒力，非保守力non-inertial frame 非惯性坐标系，非惯性系non-inverting input 非反相输入non-Newtonian fluid 非牛顿流体non-ohmic conductor 非奥姆导体non-ohmic resistor 非奥姆电阻器NOR gate 「或非」门，「非或」门normal 法线normal incidence 正入射normal reaction 法向反作用力normal stress 法向应力north pole 北极NOT gate 「非」门note 音，乐音，律音nozzle 喷嘴nuclear 原子核的nuclear energy 核能nuclear energy level 核能级nuclear fission 核裂变nuclear force 核力nuclear fusion 核聚变nuclear pile 核反应堆nuclear radiation 核辐射nuclear reaction 核反应nuclear rector 核反应堆nuclear waste 核废料nuclear weapon 核武器nucleon 核子nucleon number 核子数，质量数nucleus 原子核nuclide 核素Oobject 物，物体object distance 物距objective 接物镜，物镜obstacle 障碍物octave 八音度，倍频程Oersted 奥斯特ohm 奥姆Ohms law 奥姆定律ohmic conductor 奥姆导体ohmic resistor 奥姆电阻器ohmmeter 奥姆计oil film 油膜opaque 不透明的open circuit 断路，开路open pipe 开管open tube 开管open-loop control system 开环控制系统open-loop voltage gain 开环电压增益operating voltage 操作电压operational amplifier 运算放大器opposite phase 反相optical centre 光心optical density 光学密度optical fibre 光导纤维，光纤optical flatness 光学平度optical illusion 光幻象，视错觉optical instrument 光学仪器optical path 光程optical path difference 光程差optical system 光学系统，光具组optical thickness 光学厚度optically anisotropic 光学各向异性的optically denser medium 光密介质optically isotropic 光学各向同性的optically less dense medium 光疏介质optics 光学OR gate 「或」门orbit 轨道orbital electron 轨道电子order of magnitude 数量级ordinary ray 寻常光线orientation 取向，定向oscillation 振荡oscillator 振荡器oscillatory circuit 振荡电路oscilloscope 示波器Ostwalds viscometer 奥氏黏度计out of focus 离焦out of phase 异相output 输出output characteristic 输出特性output current 输出电流output power 输出功率output voltage 输出电压overload 超负荷，超载overtone 泛音Pp-type semiconductor p型半导体pair production 偶的产生，对的产生paraffin 石蜡parallax 视差parallel axis theorem 平行轴定理parallel beam projector 平行光束投射器parallel circuit 并联电路parallel forces 平行力parallel rays 平行光线parallel resonance 并联共振parallel resonance circuit 并联共振电路parallel-plate capacitor 平行板电容器parallelogram of forces 力平行四边形paramagnetism 顺磁性parameter 参量，参数paraxial ray 傍轴光线parent nucleus 母核parent nuclide 母核素parking orbit 驻留轨道partial polarization 部分偏振partial pressure 分压强partially polarized wave 部分偏振波particle 粒子particle movement 粒子运动，质点运动pascal 帕斯卡Paschen series 帕邢系，帕邢光谱path 路程path difference 程差peak value 峰值peak voltage 峰值电压peak-to-peak current 峰至峰电流peak-to-peak voltage 峰至峰电压pendulum 摆penetrating power 贯穿能力，贯穿本领，穿透能力，穿透本领penetration depth 贯穿深度，穿透深度percentage error 百分误差perfectly elastic 完全弹性的perfectly inelastic 完全非弹性的perigee 近地点perihelion 近日点period 周期periodic fading 周期性衰退periodic motion 周期运动periodic table 周期表periscope 潜望镜permanent magnet 永久磁铁，永磁体permeability 磁导率permeability of free space 真空磁导率permittivity 电容率，介电常数permittivity of free space 真空电容率perpendicular axis theorem 垂直轴定理，正交轴定理perpendicular distance 垂直距离Perrin tube 佩林管perspex 有机玻璃phase 相，相位phase angle 相角phase constant 相位常数，相位常量phase difference 相差，相位差phase lag 相位滞后phase lead 相位超前phasor 相矢量，相向量phon 方photo-timing gate 光控计时门photo-transistor 光敏晶体管photocell 光电池photodiode 光电二极管photoelasticity 光测弹性photoelectric cell 光电池photoelectric current 光电流photoelectric effect 光电效应photoelectric threshold 光电阈photoelectron 光电子photographic negative 照相底片photographic plate 照相底片，感光片photon 光子photosensitive 光敏的photosensitive surface 光敏面physical optics 物理光学physical property 物理性质physical quantity 物理量pick-up 拾音器，拾音piston 活塞pitch 螺距，音高，音调高度，音调Pitot tube 皮托管pivot 支点，支枢Planck constant 普朗克常数，普朗克常量plane mirror 平面镜plane of polarization 偏振面plane polarization 平面偏振plane polarized wave 面偏振波plane wave 平面波planetary motion 行星运动plano-concave lens 平凹透镜plano-convex lens 平凸透镜plastic deformation 塑性形变platinum resistance thermometer 铂阻温度计plug 插硕plutonium ?point action 尖端作用point charge 点电荷point mass 点质量point of application of force 施力点point of incidence 入射点point source 点源pointer 指针Poiseuilles formula 泊肃叶公式Poissons ratio 泊松比polar 极性polarity 极性polarization 偏振，极化polarization grille 偏振栅polarized light 偏振光polarized wave 偏振波polarizer 起偏振器，偏振器polarizing angle 起偏振角，偏振角polarizing filter 起偏振滤波器，偏振滤波器polaroid 偏振片pole 极polonium 钋polyatomic molecule 多原子分子polyethylene 聚乙烯polygon of forces 力多边形polystyrene bead 聚苯乙烯珠polystyrene cup 聚苯乙烯杯polythene strip 聚乙烯片positive charge 正电荷positive feedback 正反馈positive ion 正离子positive supply rail 正供电轨positive terminal 正端钮，正接线柱potential barrier 势垒，位垒potential difference 电势差，电位差potential divider 分压器potential energy 势能，位能potential gradient 势梯度，位梯度potentiometer 分压器，电势差计，电位差计power 功率power amplifier 功率放大器power distribution 配电power factor 功率因子power generation 发电power loss 功率损失power pack 电源箱power rating 电功率额定值power station 电力站，发电厂power supply 电源，供电power supply unit 供电设备，电源箱power transistor 功率晶体管power transmission 输电pressure 压强pressure cooker 高压锅，加压蒸煮器pressure gauge 压强计pressure law 气压定律pressurised water reactor 压水式反应堆primary coil 原线圈primary current 原电流primary voltage 原电压primary winding 原绕组principal axis 主轴principal focus 主焦点principle 原理principle of flotation 浮体原理principle of moments 力矩原理principle of superposition 迭加原理prism 棱镜prismatic periscope 棱镜潜望镜probe 深测器progressive wave 前进波projectile 抛体，抛射体projectile motion 抛体运动projection 投影，投射，抛射projector 投影机，放映机，投射器prong 音叉臂proof plane 验电板propagation 传播propeller 推进器property 性质proportionality constant 比例常数，比例常量protactinium 镤protective screen 防护屏proton 质子proton number 质子数pseudo-force 假力，伪力pulley 滑轮pulse 脉冲pump 泵pupil 瞳孔pure note 纯音push-button switch 按钮开关pyrometer 高温计QQ-factor Q因素quality of note 音品，音质quantity of electricity 电量quantization 量子化quantum 量子quantum number 量子数quarter-wave aerial 四分之一波长天线quartz 石英quenching agent 猝灭剂quiescent condition 静止状态Rradial acceleration 径向加速度radial component 径向分量radial field 辐向场，径向场radiation 辐射，放射radiation hazard 辐射危害性radiation protection 辐射防护radiator 散热器，辐射器，辐射体radio frequency 射频，无线电广播频率radio telescope 射电望远镜radio wave 无线电波radioactive 放射性radioactive decay 放射衰变radioactive disintegration 放射性蜕变radioactive fall-out 放射尘radioactive isotope 放射性同位素radioactive nucleus 放射性核radioactive series 放射系radioactive source 放射源radioactive waste 放射性废料radioactivity 放射现象，放射学radioisotope 放射性同位素radiometer 辐射计radionuclide 放射性核素radiotherapy 放射疗法radium 镭radius of curvature 曲率半径radius of gyration 回转半径，回旋半径radon 氡rail 路轨random 无规，随机random error 随机误差random motion 无规运动，随机运动random nature 无规性，随机性random walk 无规行走，随机游动range 范围，射程，量程rarefaction 疏部，稀疏rate of decay 衰变率rate of disintegration 蜕变率ratemeter 定率计rating 额定值ray 光线ray box 光线箱ray diagram 光线图Rayleighs criterion 瑞利判据reactance 电抗reaction 反作用，反作用力reactive component 抗性分量，无功分量reactor 反应堆reactor core 反应堆堆芯reading error 读数误差real depth 实深real expansion 实膨胀，真膨胀real focus 实焦点real gas 真实气体real image 实像real object 实物，实物体real-is-positive convention 实正虚负法则recoil 反冲，弹回rectification 整流rectifier 整流器rectilinear motion 直线运动rectilinear propagation 直线传播red shift 红移reed 簧片reed relay 簧片继电器reed witch 簧片开关reference frame 参考坐标系，参考系reference level 参考级reflectance 反射比reflected ray 反射线reflected wavefront 反射波阵面，反射波前reflecting telescope 反射望远镜reflection 反射reflection grating 反射光栅refracted ray 折射线refracted wavefront 折射波阵面，折射波前refracting angle 折射棱角refracting telescope 折射望远镜refraction 折射refractive index 折射率refrigerator 冰箱regular reflection 单向反射relative density 相对密度relative motion 相对运动relative permeability 相对磁导率relative permittivity 相对电容率，相对介电常数relative velocity 相对速度relativity 相对论，相对性relay 继电器relay coil 继电器线圈relay contact 继电器触点rem 雷姆remote control 遥控repulsion 相斥repulsive force 斥力reservoir capacitor 存储电容器reset switch 复位开关resistance 电阻resistance coil 电阻线圈resistance substitution box 换值电阻箱resistance thermometer 电阻温度计resistive component 电阻分量，有功分量resistivity 电阻率resistor 电阻器resolution 分解，分辨，分辨率resolution of force 力的分解resolution of vector 矢量的'分解，向量的分解resolving power 解像能力，分辨率resonance 共振，共鸣resonance tube 共鸣管resonant frequency 共振频率resonator 共振器response time 响应时间restoring couple 回复力偶restoring force 回复力restoring torque 回复转矩resultant 合量resultant displacement 合位移resultant force 合力resultant of vector 合矢量，合向量resultant velocity 合速度retard 减速retardation 减速度retina 视网膜retort stand 铁支架，铁架reverberation 混响reverberation time 混响时间reverse biased 反向偏压reverse current 反向电流reversibility of light 光的可逆性reversible process 可逆过程reversing switch 换向开关revolution 绕转，旋转，转数Reynolds number 雷诺数rheostat 变阻器，可变电阻right-angled fork track 直角分叉径迹right-hand grip rule 右手握拳定则right-hand screw rule 右手螺旋定则rigid body 刚体rigidity 刚性，刚度，刚度系数ring circuit 环形电路ripple 水波ripple tank 水波槽rocket 火箭rolling 滚动rolling friction 滚动摩擦root-mean-square value 方均根值rotary thermometer 转动式温度计rotary-type potentiometer 旋转分压器，旋转电势差计，旋转电位差计rotating platform 旋转台rotating vector 转动矢量，转动向量rotation 旋转，自转，转动rotational energy 转动能rotational motion 旋转运动rotor 转子rubber tubing 橡胶管rule 定则，法则ruling 刻度，划线runway 跑道Rutherford scattering 卢瑟福散射Rutherfords atomic model 卢瑟福原子模型Rydberg constant 里德伯常数，里德伯常量Ssafety device 安全装置satellite 卫星satellite communication 卫星通讯saturated vapour 饱和蒸气，饱和汽saturated vapour pressure 饱和蒸气压，饱和汽压saturation 饱和saturation current 饱和电流sawtooth voltage 锯齿波电压scalar 标量，无向量scalar product 标积，无向积scale 标度，比例尺，音阶scaler 脉冲计数器scan 扫描scattering 散射scattering analogue 散射模拟scattering angle 散射角scintillation 闪烁screen 屏，幕screened lead 屏蔽导线screw 螺旋，螺丝钉screw driver 螺钉起子，螺丝批screw jack 螺旋起重器sealed radioactive source 密封放射源search coil 探察线圈second 秒second law of thermodynamics 热力学第二定律second order spectrum 第二级光谱，第二级谱secondary coil 副线圈secondary current 副电流secondary emission 次级发射secondary voltage 副电压secondary winding 副绕组Seebeck effect 塞贝克效应selective absorption 选择吸收self inductance 自感self induction 自感应semicircular glass block 半圆玻璃块semiconductor 半导体semiconductor diode 半导体二极管semolina 粗粒麦粉sensitivity 灵敏度sensor 感应器，传感器sequential logic 顺序逻辑series circuit 串联电路series resonance circuit 串联共振电路series-wound motor 串激电动机，串绕电动机set switch 设定开关shaft 轴shear force 切力，剪力shear modulus 切变模量，剪模量，剪切模量shear strength 切变强度，剪切强度shear stress 切应力，剪应力shock waves 冲击波，震波short circuit 短路short sight 近视short wave 短波shunt 分流器，分流，分路shunt-wound motor 并激电动机，并绕电动机shutter 快门，光闸sievert 希沃特sign convention 符号法则signal generator 讯号产生器significant figure 有效数字silicon 硅，硅simple harmonic motion 简谐运动simple pendulum 单摆simulation 模拟single phase a.c. generator 单相交流发电机single pulley 单滑轮single slit 单缝single trace oscilloscope 单迹示波器single-pole double-throw switch 单刀双掷开关sinusoidal wave 正弦波slab-shaped magnet 平板形磁铁slide projector 幻灯片放映机slide-wire potentiometer 滑线分压器，滑线电势差计，滑线电位差计sliding contact 滑动接触sliding friction 滑动摩擦slinky spring 软弹簧slip ring 汇电环slit 缝，狭缝slope 斜率slotted weight 有槽砝码smoke cell 烟雾盒smoothing 滤波，平流smoothing capacitor 滤波电容器，平流电容器smoothing choke 滤波扼流圈，平流扼流圈smoothing circuit 滤波电路，平流电路Snells law 斯涅耳定律socket 插座sodium lamp 钠灯soft iron 软铁soft iron core 软铁心solar cell 太阳能电池solar energy 太阳能soldering iron 烙铁solenoid 螺线管solid 固体solid phase 固相solid state 固态solidification 凝固solidifying point 凝固点somatic effect 体细胞效应sonar 声纳sonic boom 声爆sonometer 弦音计sound 声音sound intensity 声强度sound intensity level 声强级sound proofing 隔声sound track 声迹，声道sound wave 声波south pole 南极spark 火花spark counter 火花计数器specific charge 荷质比，比电荷，比荷specific heat capacity 比热容量，比热容specific heat capacity at constant pressure 定压比热容量specific heat capacity at constant volume 定容比热容量specific latent heat 比潜热specific latent heat of fusion 熔解比潜热specific latent heat of vaporization 汽化比潜热spectacles 眼镜spectral analysis 光谱分析spectral line 光谱线spectral order 光谱级spectrometer 光谱仪，分光计spectroscopy 光谱学spectrum 谱，光谱，波谱spectrum tube 光谱管specular reflection 镜面反射speed 速率speed of light 光速speed of sound 声速，音速speed-time graph 速率—时间关系线图spherical aberration 球面像差spherical lens 球面透镜spherical mirror 球面镜spherical wave 球面波spherically symmetric 球对称的spin 自旋spiral 螺线，螺旋形spiral spring 螺旋弹簧spirit level 气泡水平仪spontaneous 自发的spontaneous disintegration 自发蜕变spontaneous emission 自发发射spring 弹簧，簧片，发条spring balance 弹簧秤square wave 方波squarer 方波产生器stable equilibrium 稳定平衡stable state 稳定态stackable plug 迭加式插头standard atmospheric pressure 标准大气压强，标准大气压standard cell 标准电池standard deviation 标准偏差，标准差standard error 标准误差standing wave 驻波starter 起动器starting resistance 起动电阻starting voltage 起动电压state 态states of matter 物态static equilibrium 静态平衡static friction 静摩擦static resistance 静态电阻statics 静力学stationary wave 驻波，定态波stator 定子steady flow 稳流，定常流动steady state 稳态，定态steam 水蒸汽，蒸汽steam engine 蒸汽机steam point 汽化点，汽点steam turbine 蒸汽涡轮机steel yoke 钢轭step-down transformer 降压器step-up transformer 升压器stereophonic sound 立体声stiffness 硬挺度，抗挠性stimulated absorption 受激吸收stimulated emission 受激发射Stokes law 斯托克斯定律stop watch 秒表stop clock 秒钟stopping potential 遏止电势，遏止电位storage battery 蓄电池组storage capacitor 存储电容器stored energy 储能straight pulse 直线脉冲straight wave 直线波straight wavefront 直线波阵面，直线波前strain 应变strain gauge 应变计，应变规stray capacitance 杂散电容streamline 流线stress 应力stress-strain curve 应力—应变关系曲线stretch 伸长，紧张strobe frequency 闪频stroboscope 频闪观测器，频闪仪stroboscopic photography 频闪照相法strontium 锶stylus 唱针sub-station 电力分站sublimation 升华submerge 浸没subsonic speed 亚声速，亚音速summing amplifier 加法放大器superconductivity 超导电性superconductor 超导体supercooling 过冷superficial expansivity 面膨胀系数，面膨胀率superposition 迭加supersaturation 过饱和supersonic speed 超声速，超音速surface charge density 表面电荷密度surface energy 表面能surface tension 表面张力susceptibility 磁化率sweep 扫描，扫掠sweep rate 扫描速度switch 开关，电键switch off 截断，关闭switch on 接通，开启symbol 符号synchronization 同步syringe 针筒system 系统systematic error 规律性误差，系统误差。

核磁共振中常用的英文缩写和中文名称

NMR 中常用的英文缩写和中文名称收集了一些NMR 中常用的英文缩写,译出其中文名称,供初学者参考,不妥之处请指出,也请继续添加.相关附件NMR 中常用的英文缩写和中文名称APT Attached Proton Test 质子连接实验ASIS Aromatic Solvent Induced Shift 芳香溶剂诱导位移BBDR Broad Band Double Resonance 宽带双共振BIRD Bilinear Rotation Decoupling 双线性旋转去偶(脉冲)COLOC Correlated Spectroscopy for Long Range Coupling 远程偶合相关谱COSY ( Homonuclear chemical shift ) COrrelation SpectroscopY (同核化学位移)相关谱CP Cross Polarization 交叉极化CP/MAS Cross Polarization / Magic Angle Spinning 交叉极化魔角自旋CSA Chemical Shift Anisotropy 化学位移各向异性CSCM Chemical Shift Correlation Map 化学位移相关图CW continuous wave 连续波DD Dipole-Dipole 偶极-偶极DECSY Double-quantum Echo Correlated Spectroscopy 双量子回波相关谱DEPT Distortionless Enhancement by Polarization Transfer 无畸变极化转移增强2DFTS two Dimensional FT Spectroscopy 二维傅立叶变换谱DNMR Dynamic NMR 动态NMRDNP Dynamic Nuclear Polarization 动态核极化DQ(C) Double Quantum (Coherence) 双量子(相干)DQD Digital Quadrature Detection 数字正交检测DQF Double Quantum Filter 双量子滤波DQF-COSY Double Quantum Filtered COSY 双量子滤波COSYDRDS Double Resonance Difference Spectroscopy 双共振差谱EXSY Exchange Spectroscopy 交换谱FFT Fast Fourier Transformation 快速傅立叶变换FID Free Induction Decay 自由诱导衰减H,C-COSY 1H,13C chemical-shift COrrelation SpectroscopY 1H,13C 化学位移相关谱H,X-COSY 1H,X-nucleus chemical-shift COrrelation SpectroscopY 1H,X- 核化学位移相关谱HETCOR Heteronuclear Correlation Spectroscopy 异核相关谱HMBC Heteronuclear Multiple-Bond Correlation 异核多键相关HMQC Heteronuclear Multiple Quantum Coherence 异核多量子相干HOESY Heteronuclear Overhauser Effect Spectroscopy 异核Overhause 效应谱HOHAHA Homonuclear Hartmann-Hahn spectroscopy 同核Hartmann-Hahn 谱HR High Resolution 高分辨HSQC Heteronuclear Single Quantum Coherence 异核单量子相干INADEQUATE Incredible Natural Abundance Double Quantum Transfer Experiment 稀核双量子转移实验（简称双量子实验，或双量子谱）INDOR Internuclear Double Resonance 核间双共振INEPT Insensitive Nuclei Enhanced by Polarization 非灵敏核极化转移增强INVERSE H,X correlation via 1H detection 检测1H 的H,X 核相关IR Inversion-Recovery 反（翻）转回复JRES J-resolved spectroscopy J-分解谱LIS Lanthanide （chemical shift reagent ） Induced Shift 镧系（化学位移试剂）诱导位移LSR Lanthanide Shift Reagent 镧系位移试剂MAS Magic-Angle Spinning 魔角自旋MQ（C）Multiple-Quantum （ Coherence ）多量子（相干）MQF Multiple-Quantum Filter 多量子滤波MQMAS Multiple-Quantum Magic-Angle Spinning 多量子魔角自旋MQS Multi Quantum Spectroscopy 多量子谱NMR Nuclear Magnetic Resonance 核磁共振NOE Nuclear Overhauser Effect 核Overhauser 效应（NOE）NOESY Nuclear Overhauser Effect Spectroscopy 二维NOE 谱NQR Nuclear Quadrupole Resonance 核四极共振PFG Pulsed Gradient Field 脉冲梯度场PGSE Pulsed Gradient Spin Echo 脉冲梯度自旋回波PRFT Partially Relaxed Fourier Transform 部分弛豫傅立叶变换PSD Phase-sensitive Detection 相敏检测PW Pulse Width 脉宽RCT Relayed Coherence Transfer 接力相干转移RECSY Multistep Relayed Coherence Spectroscopy 多步接力相干谱REDOR Rotational Echo Double Resonance 旋转回波双共振RELAY Relayed Correlation Spectroscopy 接力相关谱RF Radio Frequency 射频ROESY Rotating Frame Overhauser Effect Spectroscopy 旋转坐标系NOE 谱ROTO ROESY-TOCSY Relay ROESY-TOCSY 接力谱SC Scalar Coupling 标量偶合SDDS Spin Decoupling Difference Spectroscopy 自旋去偶差谱SE Spin Echo 自旋回波SECSY Spin-Echo Correlated Spectroscopy 自旋回波相关谱SEDOR Spin Echo Double Resonance 自旋回波双共振SEFT Spin-Echo Fourier Tran sform Spectroscopy （with J modulati on）（J-调制）自旋回波傅立叶变换谱SELINCOR SELINQUATE SFORD SNR or S/NSelective Inverse Correlation 选择性反相关Selective INADEQUA TE 选择性双量子（实验）Single Frequency Off-Resonance Decoupling 单频偏共振去偶Signal-to-noise Ratio 信/ 燥比SQF Single-Quantum Filter 单量子滤波SRTCF TOCSY TORO TQF WALTZ-16 Saturation-Recovery 饱和恢复Time Correlation Function 时间相关涵数Total Correlation Spectroscopy 全(总)相关谱TOCSY-ROESY Relay TOCSY-ROESY 接力Triple-Quantum Filter 三量子滤波A broadband decoupling sequence 宽带去偶序列WATERGATE Water suppression pulse sequence 水峰压制脉冲序列WEFTZQ(C) ZQF T1T2 tmWater Eliminated Fourier Transform 水峰消除傅立叶变换Zero-Quantum (Coherence) 零量子相干Zero-Quantum Filter 零量子滤波Longitudinal (spin-lattice) relaxation time for MZ 纵向(自旋- 晶格)弛豫时间Transverse (spin-spin) relaxation time for Mxy 横向(自旋-自旋)弛豫时间T C rotational correlation time 旋转相关时间。

第三讲超短脉冲的产生

Small Milli (m) Micro (µ) Nano (n) Pico (p) Femto (f) Atto (a) 10-3 10-6 10-9 10-12 10-15 10-18
Big Kilo (k) Mega (M) Giga (G) Tera (T) Peta (P) 10+3 10+6 10+9 10+12 10+15
Mode-locker
Many pulse-shortening devices have been proposed and used.
Pulsed Pumping
Pumping a laser medium with a short-pulse flash lamp yields a short pulse. Flash lamp pulses as short as ~1 µs exist. Unfortunately, this yields a pulse as long as the excited-state lifetime of the laser medium, which can be considerably longer than the pump pulse. Since solid-state laser media have lifetimes in the microsecond range, it yields pulses microseconds to milliseconds long.
Solid-state laser media have broad bandwidths and are convenient.
Laser power
Light bulbs, lasers, and ultrashort pulses

在未来计算机对我们起到的作用英语作文

在未来计算机对我们起到的作用英语作文The Role of Computers in Shaping Our FutureIn the fast-changing world of technology, computers have played a crucial role in shaping our future. From simple calculations to complex simulations, computers have become an integral part of our daily lives. In this essay, we will explore how computers are impacting various aspects of our lives and how they are likely to shape our future.One of the most significant contributions of computers is their ability to store and process large amounts of data. With the advent of big data and artificial intelligence, computers are now able to analyze data at a speed and accuracy that was once unimaginable. This has paved the way for innovations in various fields such as healthcare, finance, and transportation. For example, in healthcare, computers are being used to analyze patient data and predict diseases before they even occur. This has not only improved the efficiency of healthcare services but also saved many lives.Computers are also revolutionizing the way we communicate and collaborate. With the rise of social media and messaging apps, we are now more interconnected than everbefore. We can easily connect with friends and family from all over the world, share information instantly, and collaborate on projects in real-time. This has brought people closer together and bridged the gap between different cultures and societies.Another important role of computers in shaping our future is their impact on education. With the introduction of online learning platforms and virtual classrooms, students can now access educational materials from anywhere in the world. This has democratized education and made it more accessible to people from all walks of life. In addition, computers are also being used to personalize learning experiences and cater to the individual needs of each student. This has improved the quality of education and helped students to learn at their own pace.In the workplace, computers have transformed the way we work and do business. From automation to data analysis, computers have made businesses more efficient and productive. For example, in manufacturing, computers are being used to control robots and machines, leading to increased productivity and reduced human errors. In addition, computers are also being used to analyze market trends and predict consumer behavior, helping businesses make informed decisions and stay ahead of their competitors.Looking ahead, the role of computers in shaping our future is only going to grow. With advancements in technologies such as quantum computing and the Internet of Things, computers are becoming more powerful and smarter than ever before. This will open up new possibilities in areas such as healthcare, transportation, and agriculture. For example, in agriculture, computers can be used to monitor crop growth, analyze soil conditions, and predict weather patterns, leading to higher yields and reduced wastage.In conclusion, computers have played a crucial role in shaping our future and will continue to do so in the years to come. From healthcare to education to business, computers have revolutionized the way we live and work. As we embrace the future of technology, it is important to harness the power of computers for the betterment of society and ensure that they are used responsibly and ethically. Only then can we truly realize the full potential of computers in shaping our future.。