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 Schroedinger 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
A symplectic reduction method for symplectic G-spaces is given in this paper without using the existence of momentum mappings. By a method similar to the above one, the arthors give a symplectic reduction method for t...A symplectic reduction method for symplectic G-spaces is given in this paper without using the existence of momentum mappings. By a method similar to the above one, the arthors give a symplectic reduction method for the Poisson action of Poisson Lie groups on symplectic manifolds, also without using the existence of momentum mappings. The symplectic reduction method for momentum mappings is thus a special case of the above results.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 Schroedinger 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.
文摘A symplectic reduction method for symplectic G-spaces is given in this paper without using the existence of momentum mappings. By a method similar to the above one, the arthors give a symplectic reduction method for the Poisson action of Poisson Lie groups on symplectic manifolds, also without using the existence of momentum mappings. The symplectic reduction method for momentum mappings is thus a special case of the above results.
