Lindblad superoperators from Wigner’s phase space continuity equation

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.