Non-Markovian dynamics in a spin star system: The failure of thermalization

TL;DR

This paper demonstrates that in a spin star system with strong non-Markovian effects, the central spin does not thermalize as expected, instead reaching a steady state influenced by its initial conditions.

Contribution

It reveals that non-Markovian dynamics can prevent thermalization in a spin star model, challenging the conventional understanding of system-bath interactions.

Findings

The bath exhibits infinite correlation time, indicating perfect memory.

The central spin's final state depends on its initial state, not just the bath temperature.

Non-Markovian effects dominate the entire dynamical process.

Abstract

In most cases, a small system weakly interacting with a thermal bath will finally reach the thermal state with the temperature of the bath. We show that this intuitive picture is not always true by a spin star model where non-Markov effect predominates in the whole dynamical process. The spin star system consists 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 is that the final state of the central spin is not the thermal state equilibrium with the bath, but a steady state which depends on its initial state.