Quantum non-Markovian behavior at the chaos border

TL;DR

This paper investigates how the non-Markovian dynamics of a qubit are influenced by the classical chaos transition in its environment, revealing enhanced memory effects at the chaos border and linking quantum behavior to classical phase space structures.

Contribution

It demonstrates the relationship between classical chaos transition regions and increased non-Markovian behavior in a coupled qubit-environment system.

Findings

Non-Markovianity peaks at the chaos border.

Maxima occur at phase space boundaries between regular and chaotic regions.

Fidelity fluctuations reflect classical phase space structures.

Abstract

In this work we study the non-Markovian behaviour of a qubit coupled to an environment in which the corresponding classical dynamics change from integrable to chaotic. We show that in the transition region, where the dynamics has both regular islands and chaotic areas, the average non-Markovian behaviour is enhanced to values even larger than in the regular regime. This effect can be related to the non-Markovian behaviour as a function of the the initial state of the environment, where maxima are attained at the regions dividing separate areas in classical phase space, particularly at the borders between chaotic and regular regions. Moreover, we show that the fluctuations of the fidelity of the environment -- which determine the non-Markovianity measure -- give a precise image of the classical phase portrait.