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

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.