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Communications in Mathematical Physics 178 (1996) 627-651

On a model for quantum friction. III. Ergodic properties of the spin-boson system

Claude-Alain Pillet 1, Vojkan Jaksic 2

(1996)

We investigate the dynamics of a 2-level atom 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. From a more philosophical point of view our results show that, contrary to the conventional wisdom, quantum dynamics can be simpler at positive than at zero temperature.

1:	Centre de Physique Théorique (CPT)
	CNRS : FR2291 – Université de Provence - Aix-Marseille I – Université de la Méditerranée - Aix-Marseille II – Université Sud Toulon Var
2:	Department of Mathematics and Statistics [Mac Gill]
	Mac Gill University

Subject

:

Physics/Mathematical Physics Mathematics/Mathematical Physics Physics/Condensed Matter/Statistical Mechanics Physics/Physics/General Physics Mathematics/Operator Algebras Mathematics/Spectral Theory

Keyword(s): return to equilibrium – quantum statistical mechanics – spin boson – Liouvillean

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From: Claude-Alain Pillet <>

Submitted on: Sunday, 19 June 2005 17:21:27

Updated on: Sunday, 19 June 2005 17:21:27