Non-markovian mesoscopic dissipative dynamics of open quantum spin chains

We study the dissipative dynamics of Nquantum spins with Lindblad generator consisting of operators scaling as fluctuations, namely with the inverse square-root of N. In the large Nlimit, 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.