On the stability of KMS states in perturbative algebraic quantum field theories

TL;DR

This paper investigates the stability of KMS states in perturbative algebraic quantum field theories, revealing conditions under which they return to equilibrium and highlighting the impact of the adiabatic limit on this stability.

Contribution

It proves the return to equilibrium for KMS states with compact support interactions and shows the failure of this property in the adiabatic limit, leading to non-equilibrium steady states.

Findings

Return to equilibrium holds with compact support interactions.

Adiabatic limit prevents convergence to free equilibrium states.

Ergodic mean converges to a non-equilibrium steady state.

Abstract

We analyze the stability properties shown by KMS states for interacting massive scalar fields propagating over Minkowski spacetime, recently constructed in the framework of perturbative algebraic quantum field theories by Fredenhagen and Lindner \cite{FredenhagenLindner}. In particular, we prove the validity of the return to equilibrium property when the interaction Lagrangian has compact spatial support. Surprisingly, this does not hold anymore, if the adiabatic limit is considered, namely when the interaction Lagrangian is invariant under spatial translations. Consequently, an equilibrium state under the adiabatic limit for a perturbative interacting theory evolved with the free dynamics does not converge anymore to the free equilibrium state. Actually, we show that its ergodic mean converges to a non equilibrium steady state for the free theory.