An Analytical Approach to Thermal and Electrical Transport in a Mesoscopic Conductor

<正> In order to consider the thermal and electrical coherent transport in a mesoscopic conductor under theinfluence 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 the numerical iterative procedure as usual, whichis convenient for us to describe the thermal and electric current flow through a mesoscopic conductor. If we study theelectron-electron interaction at the Hartree approximation level, the Hartree potential satisfies the Poisson equation andSchrodinger equation, so when we expand the action function S(x) by Planck constant h, the self-consistent potentialand the wavefunction can be solved analytically order by order, and the thermal and electrical conductance can thus beobtained readily However, we just show the quantum corrections up to the second order.