Return to equilibrium

Abstract

We study an atom with finitely many energy levels in contact with a heat bath consisting of photons (blackbody radiation) at a temperature T>0. The dynamics of this system is described by a Liouville operator, or thermal Hamiltonian, which is the sum of an atomic Liouville operator, of a Liouville operator describing the dynamics of a free, massless Bose field, and a local operator describing the interactions between the atom and the heat bath. We show that an arbitrary initial state that is normal with respect to the equilibrium state of the uncoupled system at temperature T converges to an equilibrium state of the coupled system at the same temperature, as time tends to +∞ (return to equilibrium).