04-117 Juerg Froehlich and Marco Merkli

Another return of "Return to Equilibrium" (revised) (401K, ps) Apr 16, 04

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Abstract. The property of ``{\it return to equilibrium}'' is established for a class of quantum-mechanical models describing interactions of a (toy) atom with black-body radiation, or of a spin with a heat bath of scalar bosons, under the assumption that the interaction strength is {\it sufficiently weak}. For models describing the first class of systems, our upper bound on the interaction strength is {\it independent} of the temperature $T$, (with $0<T\leq T_0<\infty$), while, for the spin-boson model, it tends to zero logarithmically, as $T\rightarrow 0$. Our result holds for interaction form factors with physically realistic infrared behaviour.\\ \indent Three key ingredients of our analysis are: a suitable concrete form of the Araki-Woods representation of the radiation field, Mourre's positive commutator method combined with a recent virial theorem, and a norm bound on the difference between the equilibrium states of the interacting and the non-interacting system (which, for the system of an atom coupled to black-body radiation, is valid for {\it all} temperatures $T\geq 0$, assuming only that the interaction strength is sufficiently weak). \end{abstract} {\bf Keywords.}\ KMS states, Weyl algebra, black body radiation, thermal field, Fermi golden rule, virial theorem, positive commutator, Mourre theory

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