Wigner dynamics for quantum gases under inhomogeneous gain and loss processes with dephasing

TL;DR

This paper develops a Wigner function-based method to analyze the density evolution and transport phenomena in open quantum gases with inhomogeneous gain, loss, and dephasing, applicable to fermionic and bosonic systems.

Contribution

It introduces a semi-classical Wigner function approach for non-interacting quantum gases with inhomogeneous dissipative processes, providing closed-form solutions in specific cases.

Findings

Accurately describes density evolution in various scenarios

Reveals transport phenomena via classical quasi-particles

Validates the approach against Gaussian jump rate models

Abstract

We present a Wigner function-based approach for the particle density evolution in fermionic and bosonic open quantum many-body systems, including the effects of dephasing. In particular, we focus on chains of non-interacting particles coupled to Lindblad baths. The dissipative processes, described by linear and quadratic jump operators, are modulated by inhomogeneous couplings. Following a semi-classical approach, we find the differential equation governing the Wigner function evolution, which can be solved in closed form in some particular cases. We check the accuracy of the Wigner approach in different scenarios (i.e. Gaussian jump rates), describing the density evolution and the transport phenomena in terms of classical quasi-particles.