Non-markovian mesoscopic dissipative dynamics of open quantum spin chains

•Mean-field dissipative dynamics.•Quantum fluctuations.•Quantum central limit theorem.•Dynamics of mesoscopic correlations.

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.