一般幂指数中心势作用下的波包回归和部分回归

利用WKB近似和自关联函数方法,我们研究了一般幂指数中心势V(r)=rk (-20)作用下波包的回归和部分回归。对于排斥势(>0, k>0), 势是一长程势,量子化能级结构中只有一个量子数,波包的回归结构和一维幂指数势的情况类似。这一结果表明能级结构相同的体系具有相同的波包回归结构。 对于吸引势,能级结构中有两个量子数, 当 k取不同的值时,波包的回归结构不同。对于库仑吸引势,波包回归和部分回归出现; 但是对于其它的k值, 经过一段时间后,波包出现坍塌。本文的研究对于探讨里德堡原子和分子中电子运动的经典极限提供了一个新的方法。     

一般幂指数中心势作用下的波包回归和部分回归

利用WKB近似和自关联函数方法,我们研究了一般幂指数中心势V(r)=γrk (-20)作用下波包的回归和部分回归.对于排斥势(γ>0, k>0), 势是一长程势,量子化能级结构中只有一个量子数,波包的回归结构和一维幂指数势的情况类似.这一结果表明能级结构相同的体系具有相同的波包回归结构.对于吸引势,能级结构中有两个量子数, 当 k取不同的值时,波包的回归结构不同.对于库仑吸引势,波包回归和部分回归出现;但是对于其它的k值, 经过一段时间后,波包出现坍塌.本文的研究对于探讨里德堡原子和分子中电子运动的经典极限提供了一个新的方法.     

Fisher information,nonclassicality and quantum revivals

Wave packet revivals and fractional revivals are studied by means of a measure of nonclassicality based on the Fisher information. In particular, we show that the spreading and the regeneration of initially Gaussian wave packets in a quantum bouncer and in the infinite square-well correspond, respectively, to high and low nonclassicality values. This result is in accordance with the physical expectations that at a quantum revival wave packets almost recover their initial shape and the classical motion revives temporarily afterward.     

Wave packet propagation in a random structure at the critical energy

By relating it to the uncertainty principle, we discuss a criterium for localization in a random potential, which is consistent with the Yoffe-Regel condition.     

The energy momentum spectrum of quantum fields

It is proved, assuming Einstein causality, that the energy-momentum spectrum of a quantum field cannot be bounded. More is known under special assumptions [1, 4]. Our main concern is the method and general applicability of the result.Research supported by ONR and NSF.     

Wave packet reduction in quantum mechanics: A model of a measuring apparatus

We investigate the problem of wave packet reduction in quantum mechanics by solving the Schrödinger equation for a system composed of a model measuring apparatusM interacting with a microscopic objects. The instrument is intended to be somewhat more realistic than others previously proposed, but at the same time still simple enough to lead to an explicit solution for the time-dependent density matrix. It turns out that,practically, everything happens as if the wave packet reduction had occurred. This is a consequence of the fact that the apparatus is made up of a very large number of microsystems interacting withs. More precisely, our model shows that the macroscopic size of a measuring apparatus can lead by itself to a density matrix for the systemM + s which is physically equivalent to the density matrix of a statistical mixture corresponding to the reduced wave packet.     

Monodromy in the quantum spherical pendulum

In this article we show that monodromy in the quantum spherical pendulum can be interpreted as a Maslov effect: i.e. as multi-valuedness of a certain generating function of the quantum energy levels.     

About collapse and revivals of two quantum oscillators in off-resonance interaction

The off-resonance effect and its influence on the reversibility between two quantum subsystems in interaction (single mode cavity field and a three-level atom in cascade configuration) are studied. The partial restoration condition is found at which these radiators can restore their diagonal moments, while the non-diagonal ones remain correlated after the interaction process.     

Volume dependence of the energy spectrum in massive quantum field theories

The low-lying energy values associated to energy eigenstates describing two stable particles enclosed in a (space-like) box of sizeL are shown to be expandable in an asymptotic power series of 1/L. The coefficients in these expansions are related to the appropriate elastic scattering amplitude in a simple and apparently universal manner. At low energies, the scattering amplitude can thus be determined, if an accurate calculation of two-particle energy values is possible (by numerical simulation, for example).     

Magnetic field effects on the quantum wire energy spectrum and Green's function

We analyze the energy spectrum and propagation of electrons in a quantum wire on a 2D host medium in a normal magnetic field, representing the wire by a 1D Dirac delta function potential which would support just a single subband state in the absence of the magnetic field. The associated Schrödinger Green's function for the quantum wire is derived in closed form in terms of known functions and the Landau quantized subband energy spectrum is examined.     

Influence of phonon dispersion and exciton spectrum on the energy spectrum of magnetopolarons in a quantum well

An analysis is made of the influence of the spatial dispersion of LO phonons and the exciton effect on the energy spectrum of magnetopolarons in a quantum well. It is shown that in optical experiments where light is incident normally on the plane of the quantum well, a discrete spectrum of magnetopolarons is observed. Both the phonon dispersion and the Coulomb attraction of an electron and a hole may lead to a shift of the discrete magnetopolaron energy levels and additional contributions to the broadening of various levels.     

Morphology effects of self-assembled quantum dots on the energy spectrum of magneto-excitons

In this paper we analyze the changes experienced by the energy spectra of a confined exciton in type II semiconductor quantum dots, considering the quantum dot as a possible functional part that, in the future devices, can be applied in spintronics, optoelectronics, and quantum information technologies. We studied the lowest energy states of an exciton (X) confined in type II InP/GaInP self-assembled quantum dot (SAQDs), with axial symmetry in the presence of a uniformly applied magnetic field in the growth direction. In our model, it is considered that the electron is located within the point of InP and the hole is in the GaInP barrier. The solution of the Schrödinger equation for this system is obtained by a variational separation process of variables in the adiabatic approximation limit and within the effective mass approximation. We study the energy levels associated with the electron and the hole, and the energy of the exciton. Due to the axial symmetry of the problem the z component of the total orbital angular momentum, L_z=l_e+l_h, is preserved and the exciton states are classified according to the values of this component. Quantum dots have a finite and variable thickness, with the purpose of analyzing the effects related to the variation of the morphology and the presence of a wet layer.     

Carrier energy spectrum and lifetime in quantum dots in electric field

The S-matrix formalism is used to perform analytical calculations of the spectrum of quasi-stationary states of charge carriers in a core-shell quantum dot. Analytical expressions are obtained for the second-order perturbative corrections to the position and half-width of a quasi-stationary energy level, and level shifts are calculated numerically for a core-shell quantum dot in the presence of an electrostatic field. The corrections to level half-width due to Stark effect are analyzed as functions of level energy and barrier thickness. It is shown that there exists a level position E _cr such that the correction δΓ to the level half-width changes sign. An analytical expression for the quadratic Stark shift in a dc-biased quantum well is found in semiclassical approximation. It is shown that the corresponding correction δΓ to half-width also changes sign as energy passes through E _cr. As an example, the Stark shift is calculated for a core-shell quantum dot in the electrostatic field of an adjacent protein molecule.     

介观金属双环系统中的持续电流和量子能谱

基于电荷的不连续性,对处于外磁场中的介观双环系统进行量子化.假设系统在电荷表象中具有变换的对称性,通过求解电流和Hamilton算符的本征值方程,给出介观金属环互感系统中的量子电流和能谱关系;分析和研究了介观金属环中量子电流和能谱的性质.结果表明,持续电流和量子能谱不仅与外磁场、介观双环参数有关,而且还明显地依赖于电荷的量子化性质.     

Lax form of the quantum mechanical eigenvalue problem

The quantum mechanical eigenvalue problem with the hamiltonian H = H₀ + tV is written as a set of dynamical equations for the eigenvalues x_n(t) and the matrix elements V_nm(t) regarding the parameter t as time. By appropriate changes of variables it can be expressed as a pair of matrix equations with the Lax form, hence we are able to write all the possible constants of the motion explicitly. Implications of these constants to the statistical properties of levels are discussed.     

The quantum Kirchhoff equation and quantum current and energy spectrum of a homogeneous mesoscopic dissipation transmission line

On the basis of quantization of charge, the loop equations of quantum circuits are investigated by using the Heisenberg motion equation for a mesoscopic dissipation transmission line. On the supposition that the system has a symmetry under translation in charge space, the quantum current and the quantum energy spectrum in the mesoscopic transmission line are given by solving their eigenvalue equations. Results show that the quantum current and the quantum energy spectrum are not only related to the parameters of the transmission line, but also dependent on the quantized character of the charge obviously.     

Wave packet theory of Coulomb scattering

Potential scattering in a Coulomb field is treated in a wave packet formalism. The Rutherford law is derived from the off energy shell CoulombT-matrix avoiding the usual divergencies due to the long range Coulomb potential.