- 95-378 Jaksic V., Pillet C.-A.
- Ergodic Properties of the Spin - Boson System
Aug 16, 95
(auto. generated ps),
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Abstract. We investigate the dynamics of a 2-level atom (or spin-1/2) coupled to a
mass-less 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
self-adjoint operator naturally associated with the system. To compute this
operator, we invoke Tomita-Takesaki theory. Once this is done we use complex
deformation techniques to study its spectrum. The corresponding zero
temperature model is also reviewed and compared.