Non-Markovian behavior of small and large complex quantum systems

TL;DR

This paper investigates the non-Markovian dynamics of quantum systems interacting with environments, revealing how spectral properties influence memory effects even in large, complex systems.

Contribution

It provides an exact calculation of the quantum channel for strongly interacting systems with random eigenvectors, highlighting two key sources of non-Markovian behavior.

Findings

Non-Markovian effects persist in large environments.

Spectral density and correlations drive memory effects.

Chaotic and regular systems exhibit distinct dynamics.

Abstract

The channel induced by a complex system interacting strongly with a qubit is calculated exactly under the assumption of randomness of its eigenvectors. The resulting channel is represented as an isotropic time dependent oscillation of the Bloch ball, leading to non-Markovian behavior, even in the limit of infinite environments. Two contributions are identified: one due to the density of states and the other due to correlations in the spectrum. Prototype examples, one for chaotic and the other for regular dynamics are explored.