一维无公度系统Aubry模型的Anderson转变

数值计算结果表明,一维无公度系统Aubry模型存在扩展态、中间态和局域态。由扩展态向局域态的转变,要经过处于势强度v=2t附近的一段过渡区。这个新的结果不同于用对偶性理论证明给出的结论,即当势强度V<2t时都是扩展态,而当V>2t时都是局域态,在V=2t存在Anderson转变。 关键词：     

体态和边缘态的电导峰

本文对有限Su-Schriefer-Heeger(SSH)晶格的能量本征态和电导问题进行求解,着重研究了引线-样品的耦合强度对其体态和边缘态电导峰的不同影响.只有在弱耦合极限下,电导峰才显示全部体态和边缘态的能量本征值;随着耦合强度的增大,全部电导峰都逐渐偏离能量本征值并变宽变低,其中边缘态的电导峰还会逐渐消失;耦合强度继续增大,剩存的电导峰又逐渐变高变窄,并在强耦合极限下与不包含两端原子的新孤立系统的能量本征值一一对应.体态和边缘态对引线-样品耦合强度变化的不同响应可作为区分边缘态与体态的有效途径,亦可作为系统中存在边缘态的重要判据.     

第一类Poschl-Teller势的非线性代数结构

在形变李代数理论的基础上,利用哈密顿算符和自然算符,构造出第一类Poschl-Teller势的非线性谱生成代数。该非线性代数能够完全确定势场的能量本征态集合和本征值谱,在适当的非线性算符变换下可以化为谐振子代数,显示了该系统具有新的对称性。     

美国研究生《近代物理》考题分析(三)

第三部分少见的、灵活性大的和难度大的题目 (I)少见类型 所谓少见,我们指的是一般考生平常很少遇到的题目类型。 例9,一个质量为m的粒子在对数势 中运动。试证明 a)所有本征态具有相同的平均平方速度。求出这个平均平方速度。 b)任二能级间的间隔与质量m无关。 证明 a)速度算符v为根据Virial定理:将V(r)表达式代入上式,得到由此式可见所有本征态具有相同的平均平方速度,都等于c/m。 6)粒子的哈密顿算符为相应任一能量本征态ψi的能量本征值Ei为对于任意二能级Ek、El,我们有即任意二能级间隔Ek-Ei与m无关。 [简评]本例用通常解Schroding…     

Debye屏蔽自洽势下Au50+离子的能级与振子强度

以惯性约束聚变实验中感兴趣的金的类铜离子(Au⁵⁰⁺)为例，讨论了等离子体中自由电子对复杂原子中电子行为的影响.采用受Debye屏蔽的Hartree-Fock-Slater自洽势，计算了Au⁵⁰⁺离子的主量子数n从1到7的28个本征态，得到了对应于一系列Debye长度Λ的能量本征值E_nl，即轨道束缚能，和能级之间的光学振子强度.与类氢情况相似：自由电子的屏蔽作用使所有能级均从无屏蔽时的位置向连续态移动，即电离限下移；对于每个能量本征态(n, 关键词：     

第一类PschlTeller势的非线性代数结构

在形变李代数理论的基础上 ,利用哈密顿算符和自然算符 ,构造出第一类P schl Teller势的非线性谱生成代数 .该非线性代数能够完全确定势场的能量本征态集合和本征值谱 ,在适当的非线性算符变换下可以化为谐振子代数 ,显示了该系统具有新的对称性     

单粒子本征波函数的对称性与势形状

以单核子在原子核三轴椭球形变势中运动的本征值方程为例,说明核形状决定了核势的形状,核势形状的对称性决定了在其势中运动的单粒子本征态的对称性.当核势形状的对称性随形变参量的改变而改变时,对应单粒子本征态对称性的改变,可以用量子力学中的表象变换来表现,也可以用波函数的表象变换来认识.此问题虽然来自于原子核结构理论,但其思想对于在原子、分子、团族粒子等量子体系中处于平均场中运动的独立粒子问题具有普遍意义.     

基于实稳定方法求解单粒子共振态的Wigner函数

利用坐标空间的实稳定方法,求解了一维势场中单粒子散射态与其中共振态的本征值问题,由得到的单粒子本征波函数进一步给出相应的Wigner函数,分析了单粒子散射态与其中共振态的相空间分布特征.发现除了本征能量与本征波函数存在差异,Wigner函数在相空间的具体分布行为也可用于区分单粒子共振态与一般的散射态,在相关的量子测量实验中可能用作确定量子态的特征判据.     

在局域子空间中计算给定范围内的能量本征值

通过能量算符δ函数作用于完全随机格点波函数,构造了可用于直接计算给定范围[Emin,Emax]内能量本征值和本征函数的局域子空间.在非正交局域基下详细推导了交迭积分和哈密顿算符在分立位置表象中的表示,讨论了广义本征值问题的解法.以Morse势和Henon-Heiles势的多个能量范围为例检验了算法     

Aubry模型Anderson转变区与波矢的关系

在以前工作^{［７，８］}的基础上，我们进一步研究了一维无公度系统Ａｕｂｒｙ模型Ａｎｄｅｒｓｏｎ转变区与波矢的关系。数值结果表明：该转变区与波矢有关；波矢值愈小，该转变区处于愈低的势强度Ｖ值的范围。 关键词：     

Relation Between the Anderson Transition Zone and the Wave Vector in the Aubry Model

In a previous work of ours the numerical results have proved that there exists the Anderson transition zone in the Aubry model of one-dimensional incommensurate systems. In this paper, we further investigate the relation between the Anderson transition zone and the wave vector in this model. Our numerical results show that the Anderson transition zone is relative immediately to the wave vector, that is to say, the smaller the wave vector, the lower the value of the potential strength V in which the Anderson transition zone lies.     

ANDERSON TRANSITION ZONE IN THE SOUKOULIS-ECONOMOU MODEL OF ONE-DIMENSIONAL INCOMMENSURATE SYSTEMS

Using numerical calculation method, we have studied the Anderson transition in the Soukoulis-Economou model of one-dimensional incommensurate systems. Our results in-dicate that the Anderson transition in this model should take place gradually, i.e., the transition from the extended state to the localized state should pass through a zone in which the intermediate state is located. We call it the Anderson transition zone of the Soukoulis-Economou model. This new conclusion differs from the traditional concept, which holds that the Anderson transition of the Soukoulis-Economou model occurs abruptly at the mobility edges of this model.     

Chiral phase transition and Anderson localization in the instanton liquid model for QCD

We study the spectrum and eigenmodes of the QCD Dirac operator in a gauge background given by an instanton liquid model (ILM) at temperatures around the chiral phase transition. Generically we find the Dirac eigenvectors become more localized as the temperature is increased. At the chiral phase transition, both the low lying eigenmodes and the spectrum of the QCD Dirac operator undergo a transition to localization similar to the one observed in a disordered conductor. This suggests that Anderson localization is the fundamental mechanism driving the chiral phase transition. We also find an additional temperature dependent mobility edge (separating delocalized from localized eigenstates) in the bulk of the spectrum which moves toward lower eigenvalues as the temperature is increased. In both regions, the origin and the bulk, the transition to localization exhibits features of a 3D Anderson transition including multifractal eigenstates and spectral properties that are well described by critical statistics. Similar results are obtained in both the quenched and the unquenched case though the critical temperature in the unquenched case is lower. Finally we argue that our findings are not in principle restricted to the ILM approximation and may also be found in lattice simulations.     

A one parameter fit for glassy dynamics as a quantum corollary of the liquid to solid transition

We apply microcanonical ensemble considerations to suggest that, whenever it may thermalise, a general disorder-free many-body Hamiltonian of a typical atomic system has solid-like eigenstates at low energies and fluid-type (and gaseous, plasma) eigenstates associated with energy densities exceeding those present in the melting (and, respectively, higher energy) transition(s). In particular, the lowest energy density at which the eigenstates of such a clean many body atomic system undergo a non-analytic change is that of the melting (or freezing) transition. We invoke this observation to analyse the evolution of a liquid upon supercooling (i.e. cooling rapidly enough to avoid solidification below the freezing temperature). Expanding the wavefunction of a supercooled liquid in the complete eigenbasis of the many-body Hamiltonian, only the higher energy liquid-type eigenstates contribute significantly to measurable hydrodynamic relaxations (e.g. those probed by viscosity) while static thermodynamic observables become weighted averages over both solid- and liquid-type eigenstates. Consequently, when extrapolated to low temperatures, hydrodynamic relaxation times of deeply supercooled liquids (i.e. glasses) may seem to diverge at nearly the same temperature at which the extrapolated entropy of the supercooled liquid becomes that of the solid. In this formal quantum framework, the increasingly sluggish (and spatially heterogeneous) dynamics in supercooled liquids as their temperature is lowered stems from the existence of the single non-analytic change of the eigenstates of the clean many-body Hamiltonian at the equilibrium melting transition present in low energy solid-type eigenstates. We derive a single (possibly computable) dimensionless parameter fit to the viscosity and suggest other testable predictions of our approach.     

Delocalization and Heisenberg's uncertainty relation

In the one-dimensional Anderson model the eigenstates are localized for arbitrarily small amounts of disorder. In contrast, the Aubry-André model with its quasiperiodic potential shows a transition from extended to localized states. The difference between the two models becomes particularly apparent in phase space where Heisenberg's uncertainty relation imposes a finite resolution. Our analysis points to the relevance of the coupling between momentum eigenstates at weak potential strength for the delocalization of a quantum particle. Received 3 May 2002 / Received in final form 2 October 2002 Published online 29 November 2002     

Role of the incipient Anderson transition in electronic energy transfer in mixed organic crystals

The role of disorder in impurity bands in mixed organic crystals is examined in terms of the Anderson model. A coherent potential approximation is used to calculate averaged Green's functions; the L(E) criterion is employed to study the transition in the nature of the eigenstates. The transition is found to take place at a concentration c?, which is qualitatively in agreement with experiments. Our interpretation of the experimental results indicate a continuous variation of the transport properties above c?. Electronic energy transfer experiments in mixed organic solids can give a unique opportunity to study basic questions of localization effects.     

Resonant localized states and quantum percolation on random chains with power-law-diluted long-range couplings

We investigate the nature of one-electron eigenstates in power-law-diluted chains for which the probability of occurrence of a bond between sites separated by a distance r decays as p(r) = p/r(1+σ). Using an exact diagonalization scheme and a phenomenological finite-size scaling analysis, we determine the quantum percolation transition phase diagram in the full parameter space (p,σ). We show that the density of states displays singularities at some resonance energies associated with degenerate eigenstates localized in a pair of sites with special symmetries. This model is shown to present an intermediate phase for which there is classical percolation but no quantum percolation. Quantum percolation only takes place for σ < 0.78, a value larger than the corresponding one for the Anderson transition in long-ranged coupled chains with random diagonal disorder. The fractality of critical wavefunctions is also characterized.     

Localized and extended states in a disordered trap

We study Anderson localization in a disordered potential combined with an inhomogeneous trap. We show that the spectrum displays both localized and extended states, which coexist at intermediate energies. In the region of coexistence, we find that the extended states result from confinement by the trap and are weakly affected by the disorder. Conversely, the localized states correspond to eigenstates of the disordered potential, which are only affected by the trap via an inhomogeneous energy shift. These results are relevant to disordered quantum gases and we propose a realistic scheme to observe the coexistence of localized and extended states in these systems.