Physics – Mathematical Physics
Scientific paper
2010-05-06
Physics
Mathematical Physics
23 pages, v2-->v3: Revised version: The explanatory section 1.7 has changed and Section 3.2 has been made more explicit
Scientific paper
Recently, several authors studied small quantum systems weakly coupled to free boson or fermion fields at positive temperature. All the approaches we are aware of employ complex deformations of Liouvillians or Mourre theory (the infinitesimal version of the former). We present an approach based on polymer expansions of statistical mechanics. Despite the fact that our approach is elementary, our results are slightly sharper than those contained in the literature up to now. We show that, whenever the small quantum system is known to admit a Markov approximation (Pauli master equation \emph{aka} Lindblad equation) in the weak coupling limit, and the Markov approximation is exponentially mixing, then the weakly coupled system approaches a unique invariant state that is perturbatively close to its Markov approximation.
Kupiainen Antti
Roeck Wojciech de
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