Non-Markovian non-stationary completely positive open quantum system dynamics

TL;DR

This paper introduces a renewal-based model for non-Markovian, non-stationary open quantum system dynamics, revealing unique statistical properties and the persistence of quantum regression in non-stationary conditions.

Contribution

It develops a renewal approach to describe non-Markovian quantum dynamics, showing non-stationary behavior and validating a non-stationary quantum regression hypothesis.

Findings

Non-Markovian dynamics exhibit non-standard statistical properties.

System evolution is modified by measurements at arbitrary times.

Operator correlations follow the same dynamical structure as expectation values.

Abstract

By modeling the interaction of a system with an environment through a renewal approach, we demonstrate that completely positive non-Markovian dynamics may develop some unexplored non-standard statistical properties. The renewal approach is defined by a set of disruptive events, consisting in the action of a completely positive superoperator over the system density matrix. The random time intervals between events are described by an arbitrary waiting-time distribution. We show that, in contrast to the Markovian case, if one performs a system-preparation (measurement) at an arbitrary time, the subsequent evolution of the density matrix evolution is modified. The non-stationary character refers to the absence of an asymptotic master equation even when the preparation is performed at arbitrary long times. In spite of this property, we demonstrate that operator expectation values and operators correlations have the same dynamical structure, establishing the validity of a non-stationary quantum regression hypothesis. The non-stationary property of the dynamic is also analyzed through the response of the system to an external weak perturbation.