Wigner function with correlation damping

TL;DR

This paper numerically investigates how decoherence-induced reduction of correlation length affects quantum scattering by analyzing the evolution of the Wigner function in different regimes, revealing broadening effects and altered reflection and transmission probabilities.

Contribution

It introduces a numerical approach to study the impact of correlation damping on the Wigner function in quantum scattering, extending previous theoretical models.

Findings

Broadening and flattening of the Wigner function with decreasing correlation length

Reduced reflection at low energies due to decoherence effects

Reduced transmission at high energies as correlation length decreases

Abstract

We examine the effect of the decoherence-induced reduction of correlation length on a one-dimensional scattering problem by solving numerically the evolution equation for the Wigner function with decoherence proposed in [L. Barletti, G. Frosali and E. Giovannini, Journal of Computational and Theoretical Transport 47, 209 (2018)]. The numerical solution is achieved by the Splitting-Scheme algorithm. Three cases are examined, corresponding to a reflection-dominated regime, a transmission-dominated regime and an intermediate one. The dynamic evolution of the Wigner function is followed until the separation process of the reflected and of the transmitted packets is complete and it is observed for three different values of the correlation length. The outcomes show a broadening and flattening of the Wigner function which becomes progressively more pronounced as the correlation length is decreased. This results in a reduced reflection at low energies and in a reduced transmission at high energies.