Non-markovian mesoscopic dissipative dynamics of open quantum spin chains

TL;DR

This paper investigates the large-scale behavior of open quantum spin chains, revealing how mesoscopic fluctuations lead to non-Markovian dissipative dynamics with persistent correlations, contrasting microscopic Markovian evolution.

Contribution

It introduces a novel analysis of mesoscopic non-Markovian dynamics in quantum spin chains, highlighting the emergence of stable or unstable Gaussian fluctuations and long-lasting correlations.

Findings

Mesoscopic dynamics is Gaussian and non-Markovian.

Fluctuations can be stable or unstable asymptotically.

Correlations among fluctuations persist over time.

Abstract

We study the dissipative dynamics of $N$ quantum spins with Lindblad generator consisting of operators scaling as fluctuations, namely with the inverse square-root of $N$. In the large $N$ limit, the microscopic dissipative time-evolution converges to a non-Markovian unitary dynamics on strictly local operators, while at the mesoscopic level of fluctuations it gives rise to a dissipative non-Markovian dynamics. The mesoscopic time-evolution is Gaussian and exhibits either a stable or an unstable asymptotic character; furthermore, the mesoscopic dynamics builds correlations among fluctuations that survive in time even when the original microscopic dynamics is unable to correlate local observables.