Quantum potential spin-dependent

There is a general statement [17] that spin-orbit interaction in ID systems with Aharonov-Bohm geometry produces additional reduction factors in the Fourier expansion of thermodynamic or transport quantities. This statement holds for spin-orbit Hamiltonians for which the transfer matrix is factorized into spin-orbit and spatial parts. In a pure ID case the spin-orbit interaction is represented by the Hamiltonian //= a so)pxaz, which is the product of spin-dependent and spatial operators, and thus it satisfies the above described requirements. However, as was shown by direct calculation in Ref. [4], spin-orbit interaction of electrons in ID quantum wires formed in 2DEG by an in-plane confinement potential can not be reduced to the Hamiltonian H s. Instead, a violation of left-right symmetry of ID electron transport, characterized by a dispersion asymmetry parameter Aa, appears. We show now that in quantum wires with broken chiral symmetry the spin-orbit interaction enhances persistent current. 

Spin-orbit(SO) coupling is an important mechanism that influences the electron spin state [1], In low-dimensional structures Rashba SO interaction comes into play by introducing a potential to destroy the symmetry of space inversion in an arbitrary spatial direction [2-6], Then, based on the properties of Rashba effect, one can realize the controlling and manipulation of the spin in mesoscopic systems by external fields. Recently, Rashba interaction has been applied to some QD systems [6-8]. With the application of Rashba SO coupling to multi-QD structures, some interesting spin-dependent electron transport phenomena arise [7]. In this work, we study the electron transport properties in a three-terminal Aharonov-Bohm (AB) interferometer where the Rashba interaction is taken into account locally to a QD. It is found that Rashba interaction changes the quantum interference in a substantial way. 

Equation (3.1.2) is the nonrelativistic Hamiltonian. This means that the spin-dependent part of the Hamiltonian (Hso spin-orbit and Hss spin-spin) has been neglected. The electronic angular momentum quantum numbers, which are well-defined for eigenfunctions of nonrelativistic adiabatic and diabatic potential curves, are A, E, and 5 (and redundantly, Q = A + E). 

As shown by Fig. 2.9, with the inclusion of the spin-orbit interaction, the observed magic numbers were properly reproduced. The spin-orbit interaction for atomic electrons is a small quantum-relativistic effect. The nuclear spin-orbit coupling is much stronger and results, in addition to relativistic effects, from the spin dependence of the nucleon-nucleon potential. 

Quantum chemical ah initio calculations haVe reached the stage where they can yield detailed quantitative information about the interaction potentials between molecules, in particular about the orientational dependence of these potentials and, in the case of open-shell molecules, also about their spin dependence. In order to use the intermolecular potentials in the calculation of aggregate properties and, thereby, to test and improve these potentials, it is necessary to express them in analytic form. Moreover, the question is important whether the intermolecular interactions are additive. These topics are addressed in the first part of this paper. 

A molecular system consists of electrons and nuclei. Their position vectors are denoted hereafter as rel and qa, respectively. The potential energy function of the whole system is V(rel, qa). For simplicity, we skip the dependence of the interactions on the spins of the particles. The nuclei, due to their larger mass, are usually treated as classical point-like objects. This is the basis for the so called Bom-Oppenheimer approximation to the Schroedinger equation. From the mathematical point of view, the qnuc variables of the Schroedinger equation for the electrons become the parameters. The quantum subsystem is described by the many-dimensional electron wave function rel q ). 

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