An Infinite Level Atom coupled to a Heat Bath

TL;DR

This paper models a system of finitely many particles with infinite energy levels interacting with an infinite heat bath, establishing the existence of dynamics and equilibrium states under specific conditions.

Contribution

It provides rigorous conditions for the existence of dynamics and KMS states in a system with infinitely many energy levels coupled to a heat bath.

Findings

Existence of the dynamics $ aug$ for the system.

Existence of a $(eta, aug)$-KMS state under explicit conditions.

Conditions on interaction strength and inverse temperature for stability.

Abstract

We consider a $W^*$-dynamical system $(\Mg,\taug)$, which models finitely many particles coupled to an infinitely extended heat bath. The energy of the particles can be described by an unbounded operator, which has infinitely many energy levels. We show existence of the dynamics $\taug$ and existence of a $(\beta,\taug)$ -KMS state under very explicit conditions on the strength of the interaction and on the inverse temperature $\beta$.