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

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.

29 pages

References in corpus (1)

• The time slice axiom in perturbative quantum field theory on globally hyperbolic spacetimes

Cited by in corpus (6)

• Equilibrium states in Thermal Field Theory and in Algebraic Quantum Field Theory
• Relative entropy and entropy production for equilibrium states in pAQFT
• Perturbative Algebraic Quantum Field Theory on Quantum Spacetime: Adiabatic and Ultraviolet Convergence
• Disjointness of inertial KMS states and the role of Lorentz symmetry in thermalization
• Secular growths and their relation to equilibrium states in perturbative QFT
• Thermal state with quadratic interaction