Eur. Phys. J. D (2013) 67: 218
https://doi.org/10.1140/epjd/e2013-40099-0

Regular Article

Non-Markovian dynamics in a spin star system: the failure of thermalisation

¹ Beijing National Laboratory for condensed matter physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, P.R. China
² School of Physics and Electronic Science, Changsha University of Science and Technology, Changsha 410114, P.R. China

^a e-mail: zhoudl72@aphy.iphy.ac.cn

Received: 25 February 2013
Received in final form: 29 May 2013
Published online: 1 November 2013

Abstract

In most cases, a small system weakly interacting with a thermal bath will eventually reach a thermal state with the temperature of the bath. We show that this intuitive picture is not always true, by using a spin star model where the non-Markov effect dominates the dynamical process. The spin star system consists of a central spin homogeneously interacting with an ensemble of identical noninteracting spins. We find that the correlation time of the bath is infinite, which implies that the bath has a perfect memory, and that the dynamical evolution of the central spin must be non-Markovian. A direct consequence of this is that the final state of the central spin is not the thermal state in equilibrium with the bath, but a steady state which depends on the initial state of the spin.