Non-Hermite Spinor Boltzmann Equation and Its Hermitization

Abstract

It is known that the Wigner distribution function in the quantum Boltzmann equation is not positive elsewhere, which causes trouble for its application to the mesoscopic transport problem. Similarly, if we extend the quantum Boltzmann equation to the spinor Boltzmann equation, which includes the spin freedom in the usual Wigner distribution, and the spinor matrix distribution function therein is not Hermite, we must make this non-Hermite spinor Boltzmann equation Hermitization. So in this paper, we propose a spinor Boltzmann equation with Hermite distribution function and then obtain the equations of continuity satisfied by the charge density, charge current, spin accumulation, and spin current. The numerical results for these physical quantities are illustrated by an example of spin-polarized transport scattered by impurities in a system of spintronics. Their differences compared with the usual spinor Boltzmann equation are shown.