Aharonov-Bohm效应和量子力学相位概念的一些问题——评曾谨言著《量子力学》卷Ⅱ第六次印刷第四章的物理概念

意图澄清一些对于Aharonov-Bohm效应的误解,指出一本国内流行甚广的量子力学教科书中对这一物理概念的错误解说.     

The Aharonov-Bohm effect and its applications to electron phase microscopy

The Aharonov-Bohm effect was conclusively established by a series of our electron interference experiments, with the help of some advanced techniques, such as coherent field-emission electron beams and microlithography. Using this fundamental principle behind the interaction of an electron wave with electromagnetic fields, new observation techniques were developed to directly observe microscopic objects and quantum phenomena previously unobservable.     

Magneto-optical specifications of Rosen-Morse quantum dot with screw dislocation

This is the first study to consider a quantum dot with screw dislocation that has Rosen-Morse (RM) confinement potential, generated by a GaAs/GaAlAs heterostructure. An external magnetic field and Aharonov-Bohm (AB) flux field were also applied on RM quantum dot (RMQD) in order to stave the effects of a screw dislocation defect. The combined effect of the screw dislocation defect, the external magnetic field, and AB flux field on the total refractive index changes (TRICs) and the total absorption coefficients (TACs) of RMQD are thus investigated. Cylindrical coordinates are used due to the direction of application of the torsion and the external fields, as well as due to the structure's symmetry. The effective mass approximation and tridiagonal matrix methods are used in order to obtain the subband energy spectra and electronic wave functions of RMQD. The nonlinear optical specifications of RMQD are checked using compact-density-matrix formalism within the framework of the iterative method. Reviews without screw dislocation are also carried out in order to be able to clarify the effects of a screw dislocation defect on the optical properties, and then, both cases are deliberated. This study is the first attempt to analyze the AB flux field for RMQD without screw dislocation. In the present study, the influences of a screw dislocation defect on RMQD's TRICs and TACs are probed by considering different values of the external magnetic field and AB flux field, and the ranges of corresponding parameters on the optimum of the structure are specified. Moreover, the study also elucidates how to rule out the effects of screw dislocation on optical specifications by means of the external fields. Despite a certain screw dislocation, the frequency range is determined where the structure behaves as if it is perfect (namely, without screw dislocation) for its optimum, which in turn is crucial for experimental applications.     

Time-Dependent 2D Harmonic Oscillator in Presence of the Aharanov-Bohm Effect

We use the Lewis-Riesenfeld theory to determine the exact form of the wavefunctions of a two-dimensionnal harmonic oscillator with time-dependent mass and frequency in presence of the Aharonov-Bohm effect (AB). We find that the auxiliary equation is independent of the AB magnetic flux. In the particular case of quantized AB magnetic flux the wavefunctions coincide exactly with the wavefunctions of the 2D time-dependent harmonic oscillator. PACS: 03.65Ge; 03.65Fd; 03.65Bz     

Optically mediated spin current and Fano resonance in an Aharonov-Bohm ring with a quantum dot

We study the spin-polarized transport and Fano resonance in an Aharonov-Bohm (AB) interferometer with an embedded quantum dot, where the dot is irradiated by continuous circularly polarized light. Compared with the conventional Fano form, the resonance line shape is found to be deformed by the interplay between the external irradiation and the Coulomb repulsion. The Fano resonance peaks are split due to the shift of the effective energy level in the dot by Rabi oscillation of electron-heavy hole pairs. The direction and magnitude of spin current polarization can be modulated by the device parameters. Furthermore, the direct tunneling between two leads can induce a sharp sign reversal of spin polarization, the system thus operates as a rectifier for spin current polarization.     

Eccentricity effects on the quantum confinement in double quantum rings

This work presents a theoretical study of the energy spectrum of GaAs/AlGaAs concentric double quantum rings, under an applied magnetic field directed perpendicular to the ring plane. The Schrödinger equation for this system is solved in a realistic model consisting of rings with finite barrier potentials. Numerical results show that increasing the magnetic field intensity leads to oscillations in the ground state energy which, in contrast to the usual Aharonov-Bohm oscillations, do not have a well defined period, due to the coupling between inner and outer ring states. However, when one considers an elliptical geometry for the rings, the energy spectra of the inner and outer ring states are decoupled and the periodicity of the oscillations is recovered.     

Quantum and Classical Disparity and Accord

Discrepancies and accords between quantum (QM) and classical mechanics (CM) related to expectation values and periods are generally found for both the harmonic oscillator (SHO) and a free particle in a box (FPB), which may apply generally. These indicate non-locality is expected throughout QM. The FPB energy states violate the Correspondence Principle. Previously unexpected accords are found and proven that 〈x ²〉 _CM =〈x ²〉 _QM and τ _CM =τ _QMb (beat period i.e. beats between the phases for adjoining energy states) for the SHO for all quantum numbers, n. However, for the FPB the beat periods differ at small n. It is shown that a particle’s velocity in an infinite square well varies, no matter how wide the box, nor how far the particle is from the walls. The quantum free particle variances share an indirect commonality with the Aharonov-Bohm and Aharonov-Casher effects in that there is a quantum action in the absence of a force. The concept of an “Expectation Value over a Partial Well Width” is introduced. This paper raises the question as to whether these inconsistencies are undetectable, or can be empirically ascertained. These inherent variances may need to be fixed, or nature is manifestly more non-classical than expected.     

量子环上的负电荷激子

讨论了负电荷激子X^-的能-光谱及其Aharonov-Bhom振荡.负电荷激子是三个带电粒子组成的体系,其基函数（基矢）数目大,数值计算艰巨. 以往人们常把体系的空间波函数分离成质心运动和相对运动两部分来处理,这种方法误差大,只适用于外加磁场很小的情况.直接由体系的Hamilton量出发,基于角动量守恒,把基矢按总角动量分类. 据此提出了一种简便的求解体系的本征矢和本征函数方案,使用该方法使计算时间节省了90%以上.所得计算结果没有抗磁现象,且计算结果与现有的实验数据符合很好.还讨论了环的半径、介质电容率和空穴的有效质量与ABO的关系. 关键词： 量子环 负电荷激子 能-光谱 Aharonov-Bhom振荡     

Separable-entangled frontier in a bipartite harmonic system

We consider a statistical mixture based on that of two identical harmonic oscillators which is characterized by four parameters, namely, the concentrations (x and y) of diagonal and nondiagonal bipartite states, and their associated thermal-like noises (T/α and T, respectively). The fully random mixture of two spins 1/2 as well as the Einstein-Podolsky-Rosen (EPR) state are recovered as particular instances. By using the conditional nonextensive entropy as introduced by Abe and Rajagopal, we calculate a bound for the separable-entangled frontier. Although this procedure is known to provide a necessary but in general not sufficient condition for separability, it does recover, in the particular case x = T = 0 ( ∀α), the 1/3 exact result known as Peres' criterion. The x = 0 frontier remarkably resembles to the critical line associated with standard diluted ferromagnetism where the entangled region corresponds to the ordered one and the separable region to the paramagnetic one. The entangled region generically shrinks for increasing T or increasing α. Received 18 April 2002 / Received in final form 11 July 2002 Published online 31 October 2002 RID="a" ID="a"e-mail: celia@cbpf.br     

Topological phase interference effects in resonant quantum tunneling of the Néel vector between nonequivalent magnetic wells in mesoscopic single-domain antiferromagnets

Resonant quantum tunneling of the Néel vector between nonequivalent magnetic wells is investigated theoretically for a nanometer-scale single-domain antiferromagnet with biaxial crystal symmetry in the presence of an external magnetic field applied along the easy anisotropy axis, based on the two-sublattice model. Both the Wentzel-Kramers-Brillouin exponent and the preexponential factors are evaluated in the instanton contribution to the tunneling rate for finite and zero magnetic fields by applying the instanton technique in the spin-coherent-state path-integral representation, respectively. The quantum interference or spin-parity effects induced by the topological phase term in the Euclidean action are discussed in the rate of quantum tunneling of the Néel vector. In the absence of an external applied magnetic field, the effect of destructive phase interference or topological quenching on resonant quantum tunneling of the Néel vector is evident for the half-integer excess spin antiferromagnetic nanoparticle. In the weak field limit, the tunneling rates are found to oscillate with the external applied magnetic field for both integer and half-integer excess spins. We discuss the experimental condition on the applied magnetic field which may allow one to observe the topological quenching effect for nanometer-scale single-domain antiferromagnets with half-integer excess spins. Tunneling behavior in resonant quantum tunneling of the magnetization vector between nonequivalent magnetic wells is also studied for a nanometer-scale single-domain ferromagnet by applying the similar technique, but in the large noncompensation limit. Received 4 June 1999