A Non-Markovian Phase Space Approach to Schrödinger Dynamics: The Space-Time Wigner Transform

Abstract

A phase space description of Schroźdinger dynamics is provided in terms of a quantum kinetic formalism relying on the introduction of an appropriate extension of the well-known Wigner transform, also accounting for time delocalizations. This “space-time Wigner distribution,” built up in the framework of two-time correlation functions, is shown to be governed by a non-Markovian, integro-differential equation of convolution type. Its utility in investigating long time dynamics of quantum systems is also discussed and illustrated with some examples.