 95378 Jaksic V., Pillet C.A.
 Ergodic Properties of the Spin  Boson System
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Aug 16, 95

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Abstract. We investigate the dynamics of a 2level atom (or spin1/2) coupled to a
massless bosonic field at positive temperature. We prove that, at small
coupling, the combined quantum system approaches thermal equilibrium.
Moreover we establish that this approach is exponentially fast in time.
We first reduce the question to a spectral problem for the Liouvillean, a
selfadjoint operator naturally associated with the system. To compute this
operator, we invoke TomitaTakesaki theory. Once this is done we use complex
deformation techniques to study its spectrum. The corresponding zero
temperature model is also reviewed and compared.
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