Non-Markovian quantum dynamics: local versus non-local

TL;DR

This paper explores the dual descriptions of non-Markovian quantum dynamics, showing how local and non-local equations relate, and discusses how singular generators can lead to phenomena like coherence revival.

Contribution

It demonstrates the equivalence of local and non-local master equations in non-Markovian quantum systems and analyzes the physical implications of singular generators.

Findings

Local and non-local descriptions are complementary.

Singular generators can cause coherence revival.

Dynamics remain regular despite singularities.

Abstract

We analyze non-Markovian evolution of open quantum systems. It is shown that any dynamical map representing evolution of such a system may be described either by non-local master equation with memory kernel or equivalently by equation which is local in time. These two descriptions are complementary: if one is simple the other is quite involved, or even singular, and vice versa. The price one pays for the local approach is that the corresponding generator keeps the memory about the starting point `t_0'. This is the very essence of non-Markovianity. Interestingly, this generator might be highly singular, nevertheless, the corresponding dynamics is perfectly regular. Remarkably, singularities of generator may lead to interesting physical phenomena like revival of coherence or sudden death and revival of entanglement.