Lindblad Superoperators from Wigner's Phase Space Continuity Equation

TL;DR

This paper demonstrates how Lindblad superoperators naturally emerge from Wigner's phase space continuity equation for weakly interacting quantum systems, providing a straightforward derivation of the Lindblad form.

Contribution

It shows that Lindblad superoperators can be directly derived from Wigner's phase space formulation, revealing their fundamental connection.

Findings

Lindblad form arises naturally from Wigner's equation

Derivation is simple and algebraic for weakly interacting systems

Highlights the fundamental role of phase space in quantum dissipation

Abstract

For a simple quantum system weakly interacting with the environment Wigner's 1932 formulation of quantum physics can be used to derive coupling to the environment using simple algebra. We show that the correct expressions, using coupling terms of `Lindblad form', are forced upon us. This is remarkable given that it took several decades before Lindblad's result was found in 1976.