1995/08/17 by Vojkan Jakšić, Jaksic, V., Claude‐Alain Pillet +1 · 1 citation
Mathematics · Physics and Astronomy · #Adaptation and Self-Organizing Systems (nlin.AO) #Advanced Thermodynamics and Statistical Mechanics #FOS: Physical sciences #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.adap-org/9508004
openalex publication_date 1995/08/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.