Non-Markovian master equations from piecewise dynamics

TL;DR

This paper develops a broad class of non-Markovian quantum dynamical maps using piecewise evolution with random jumps, resulting in a master equation with memory effects and inhomogeneous terms, and assesses their non-Markovianity.

Contribution

It introduces a novel construction of non-Markovian quantum maps from piecewise dynamics with random jumps, leading to a new class of master equations with memory kernels.

Findings

Derived a closed evolution equation with memory kernel for the system.

Explicitly characterized the non-Markovianity through distinguishability measures.

Provided a framework for modeling open quantum systems with non-Markovian dynamics.

Abstract

We construct a large class of completely positive and trace preserving non-Markovian dynamical maps for an open quantum system. These maps arise from a piecewise dynamics characterized by a continuous time evolution interrupted by jumps, randomly distributed in time and described by a quantum channel. The state of the open system is shown to obey a closed evolution equation, given by a master equation with a memory kernel and a inhomogeneous term. The non-Markovianity of the obtained dynamics is explicitly assessed studying the behavior of the distinguishability of two different initial system's states with elapsing time.