Nonlinear Sciences – Adaptation and Self-Organizing Systems
Scientific paper
1995-08-17
Nonlinear Sciences
Adaptation and Self-Organizing Systems
31 pages, postscript
Scientific paper
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.
Jakšić Vojkan
Pillet Claude-Alain
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