Time inhomogeneous quantum dynamical maps

TL;DR

This paper explores a broad class of time inhomogeneous quantum dynamical maps, their mathematical properties, and how they generalize traditional master equations, including both memory kernel and time-local approaches.

Contribution

It introduces a new framework for time inhomogeneous quantum evolution using two-parameter maps constructed from jump processes, extending the master equation formalism.

Findings

Dynamical maps satisfy a generalized memory kernel master equation.

Time-local approaches are also applicable to these maps.

Comparison between time homogeneous and inhomogeneous scenarios is provided.

Abstract

We discuss a wide class of time inhomogeneous quantum evolution which is represented by two-parameter family of completely positive trace-preserving maps. These dynamical maps are constructed as infinite series of jump processes. It is shown that such dynamical maps satisfy time inhomogeneous memory kernel master equation which provides a generalization of the master equation involving the standard convolution. Time-local (time convolution-less) approach is discussed as well. Finally, the comparative analysis of traditional time homogeneous vs. time inhomogeneous scenario is provided.