Dynamics and thermalization in a simple mesoscopic fermionic bath

Abstract

We consider a central fermion strongly interacting with a surrounding mesoscopic bath of fermions which is weakly coupled to a Markovian bath of fermions. The master equation of the system consisting of the central fermion and the mesoscopic bath is derived, and based on this master equation, the reduced dynamics and thermalization of the central fermion are investigated. As probes for studying the dynamics and thermalization, the mean number of the central fermion and the current density are calculated. The observed dynamics reveal that strong coupling strength induces non-Markovian behavior and that in the long time limit thermalization is attained leaving the central fermion in a thermal state that is described by the corresponding Gibbs distribution. Upon attaining the thermal state, the central fermion is found to be entangled with the collective mode of the surrounding mesoscopic bath in the high-temperature regime, whereas in the low-temperature regime, it is found to undergo sudden death of entanglement.