Abstract
In order to consider the thermal and electrical coherent transport in amesoscopic conductor under the influence of electron-electron interaction,in this paper, we establish a method in terms of which one can analyticallyobtain the Hartree self-consistent potential instead of computing it by thenumerical iterative procedure as usual, which is convenient for us todescribe the thermal and electric current flow through a mesoscopicconductor. If we study the electron-electron interaction at the Hartreeapproximation level, the Hartree potential satisfies the Poisson equationand Schrödinger equation, so when we expand the action function S(x)by Planck constant ℏ, the self-consistent potential and thewavefunction can be solved analytically order by order, and the thermal andelectrical conductance can thus be obtained readily. However, we just showthe quantum corrections up to the second order.
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