In order to consider the thermal and electrical coherent transport in a mesoscopic conductor under the influence of electron-electron interaction, in this paper, we establish a method in terms of which one can analyti...In order to consider the thermal and electrical coherent transport in a mesoscopic conductor under the influence of electron-electron interaction, in this paper, we establish a method in terms of which one can analytically obtain the Hartree self-consistent potential instead of computing it by the numerical iterative procedure as usual, which is convenient for us to describe the thermal and electric current flow through a mesoscopic conductor. If we study the electron-electron interaction at the Hartree approximation level, the Hartree potential satisfies the Poisson equation and Schrodinger equation, so when we expand the action function S(x) by Planck constant h, the self-consistent potential and the wavefunction can be solved analytically order by order, and the thermal and electrical conductance can thus be obtained readily. However, we just show the quantum corrections up to the second order.展开更多
Macroscopic polarization differences in crystal dielectrics have been accurately treated by certain authors using the geometric phase approach.However,in their treatments the explicit meaning of the slowly varying par...Macroscopic polarization differences in crystal dielectrics have been accurately treated by certain authors using the geometric phase approach.However,in their treatments the explicit meaning of the slowly varying parameters was not explored.In this paper we restudy the problem under the Born-Oppenheimer approximation.It turns out that the coordinates of nuclei in the system can be taken as the slowly varying parameters.In addition,our treatment is no longer restricted to the case of null electric held.展开更多
A description of geometric phase in terms of path integral formalism is presented.It is proved that this adiabatic phase can appear in the propagator or Green function of an adiabatic system.In the semiclassical appro...A description of geometric phase in terms of path integral formalism is presented.It is proved that this adiabatic phase can appear in the propagator or Green function of an adiabatic system.In the semiclassical approximation,following the Green function expression of the electronic density of states,the corresponding generalized Bohr-Sommerfeld quantisation rule can thus be obtained.It is shown that this rule has been corrected by the geometric phase.展开更多
文摘In order to consider the thermal and electrical coherent transport in a mesoscopic conductor under the influence of electron-electron interaction, in this paper, we establish a method in terms of which one can analytically obtain the Hartree self-consistent potential instead of computing it by the numerical iterative procedure as usual, which is convenient for us to describe the thermal and electric current flow through a mesoscopic conductor. If we study the electron-electron interaction at the Hartree approximation level, the Hartree potential satisfies the Poisson equation and Schrodinger equation, so when we expand the action function S(x) by Planck constant h, the self-consistent potential and the wavefunction can be solved analytically order by order, and the thermal and electrical conductance can thus be obtained readily. However, we just show the quantum corrections up to the second order.
基金Supported by the National Natural Science Foundation of China under Grant No.19677101.
文摘Macroscopic polarization differences in crystal dielectrics have been accurately treated by certain authors using the geometric phase approach.However,in their treatments the explicit meaning of the slowly varying parameters was not explored.In this paper we restudy the problem under the Born-Oppenheimer approximation.It turns out that the coordinates of nuclei in the system can be taken as the slowly varying parameters.In addition,our treatment is no longer restricted to the case of null electric held.
基金Supported by the National Natural Science Foundation of China under Grant No.19677101.
文摘A description of geometric phase in terms of path integral formalism is presented.It is proved that this adiabatic phase can appear in the propagator or Green function of an adiabatic system.In the semiclassical approximation,following the Green function expression of the electronic density of states,the corresponding generalized Bohr-Sommerfeld quantisation rule can thus be obtained.It is shown that this rule has been corrected by the geometric phase.
