Wigner-Lindblad equations for quantum friction

TL;DR

This paper develops a quantum model of friction using a translation-invariant Lindblad equation, successfully capturing dissipative effects and approximate equilibration, thus addressing a longstanding challenge in quantum dissipation modeling.

Contribution

It introduces the first translation-invariant Lindblad equation that models quantum friction consistent with classical dynamics and Ehrenfest relations.

Findings

Model approximately equilibrates in simulations

Advances the development of quantum friction models

Opens new avenues for dissipation phenomena exploration

Abstract

Dissipative forces are ubiquitous and thus constitute an essential part of realistic physical theories. However, quantization of dissipation has remained an open challenge for nearly a century. We construct a quantum counterpart of classical friction, a velocity-dependent force acting against the direction of motion. In particular, a translationary invariant Lindblad equation is derived satisfying the appropriate dynamical relations for the coordinate and momentum (i.e., the Ehrenfest equations). Numerical simulations establish that the model approximately equilibrates. These findings significantly advance a long search for a universally valid Lindblad model of quantum friction and open opportunities for exploring novel dissipation phenomena.