Analytical results for the non-Markovianity of quantum spin ensembles

We study the non-Markovian character of spin ensembles. The ensemble is assumed to be isolated and a subset of spins is taken as the system, while the remaining part of the ensemble is taken as the environment. For a large class of interaction range, we derive analytical expressions for the non-Markovianity [1] following a recently introduced measure [2]. In particular, we investigate the thermodynamic limit and derive conditions to observe a Markovian dynamics or not. For a system of a single spin, it is explicitly shown that our results agree with the other known measures of non-Markovianity. We believe that our work can be used to investigate further the dynamics of fundamental models in condensed matter physics from the new perspective of (non-)Markovianity.
[1] R. Dubertrand, A. Cesa, J. Martin, to be submitted
[2] S. Lorenzo, F. Plastina, and M. Paternostro, Phys. Rev. A 88 (2013)