A Wigner-Lindblad phase space model for open quantum dynamics

Abstract

We investigate the collisional quantum dynamics of an open system in contact with a thermal bath. We propose a particle-bath interaction model based on the Weyl quantization principle and the Wigner phase space description of quantum evolution. By factorizing the reduced Hamiltonian of the open system via supersymmetric quantum mechanics techniques, we construct system-dependent creation and annihilation operators for arbitrary potential landscapes. This allows us to extend the classical Fokker--Planck relaxation mechanism to incorporate Lindblad quantum stochastic jumps within the Wigner phase-space formalism. Through a semiclassical expansion of the Moyal star product to second order, we obtain a generalized Wigner--Lindblad kinetic model featuring position-dependent friction and diffusion terms. We establish the mathematical well-posedness of the Lindblad problem and we validate our approach through numerical simulations. Our model resolves unphysical long-time artifacts of standard quantum Fokker--Planck models in quartic double-well traps, accurately captures dissipative quantum state localization in 2D molecular potentials (4D phase space), and effectively evaluates electron transport and trapping times in InAs/InP resonant tunneling diodes.