An Analytical Solution for the Wigner-Boltzmann Transport Equation in the Relaxation Time Approximation

TL;DR

This paper presents an analytical solution to the Wigner-Boltzmann transport equation under the relaxation time approximation, improving upon numerical methods and addressing unphysical features in previous boundary condition schemes.

Contribution

It introduces an analytical approach to solving the quantum Wigner-Boltzmann equation with constant relaxation time, enhancing accuracy and physical consistency.

Findings

Analytical solution derived for the Wigner-Boltzmann equation

Method avoids unphysical features of previous boundary schemes

Provides a more reliable tool for quantum energy dissipation analysis

Abstract

The quantum version of the Boltzmann transport equation (Wigner-Boltzmann equation) is a quite useful tool to investigate the effects of energy dissipation in quantum systems. Numerical approaches uses to be employed in order to stablish a suitable solution. In this paper, an analytical solution is shown to exist when the constant relaxation time approximation is considered. The formalism presented here is capable to avoid some unphysical features early reported in literature for the conventional boundary condition scheme.