Quantum non-Markovianity and localization

TL;DR

This paper investigates how the degree of non-Markovianity in a quantum system relates to the localization of its environment, revealing complex relations in integrable regimes and simpler patterns in chaotic regimes.

Contribution

It introduces a detailed analysis of non-Markovianity measures in a qubit-spin chain system, highlighting the influence of environmental localization and chaos on non-Markovian behavior.

Findings

Non-Markovianity does not have a simple relation with localization in integrable regimes.

Approaching chaos reveals clearer relations between non-Markovianity and localization.

The pattern of non-Markovianity in parameter space is robust under different interaction Hamiltonians.

Abstract

We study the behavior of non-Markovianity with respect to the localization of the initial environmental state. The "amount" of non-Markovianity is measured using divisibility and distinguishability as indicators, employing several schemes to construct the measures. The system used is a qubit coupled to an environment modeled by an Ising spin chain kicked by ultra-short pulses of a magnetic field. In the integrable regime, non-Markovianity and localization do not have a simple relation, but as the chaotic regime is approached, simple relations emerge, which we explore in detail. We also study the non-Markovianity measures in the space of the parameters of the spin coherent states and point out that the pattern that appears is robust under the choice of the interaction Hamiltonian but does not have a KAM-like phase-space structure.