Synchro-thermalization of composite quantum system

TL;DR

This paper investigates how a composite quantum system can reach thermal equilibrium even when only part of it contacts a heat bath, highlighting the importance of energy level connectivity and factors affecting relaxation speed.

Contribution

It demonstrates that a composite quantum system can thermalize through internal connectivity even with limited bath contact, and analyzes relaxation speed suppression factors.

Findings

Whole composite can thermalize if energy levels are connected.

Relaxation speed is suppressed by multi-Franck-Condon factors.

Connectivity of energy levels is crucial for thermalization.

Abstract

We study the thermalization of a composite quantum system consisting of several subsystems, where only a small one of the subsystem contacts with a heat bath in equilibrium, while the rest of the composite system is contact free. We show that the whole composite system still can be thermalized after a relaxation time long enough, if the energy level structure of the composite system is connected, which means any two energy levels of the composite system can be connected by direct or indirect quantum transitions. With an example where an multi-level system interacts with a set of harmonic oscillators via non-demolition coupling, we find that the speed of relaxation to the global thermal state is suppressed by the multi-Franck-Condon factor due to the displacements of the Fock states when the degrees of freedom is large.