SPECTRAL THEORY OF THERMAL RELAXATION

We review some results obtained in a recent series of papers on therma l relaxation in classical and quantum dissipative systems. We consider models where a small system T, with a finite number of degrees of fre edom, interacts with a large environment R in thermal equilibrium at p ositive temperature T. The zeroth law of thermodynamics postulates tha t, independently of its initial configuration, the system T approaches a unique stationary state as t-->infinity. By definition, this limiti ng state is the equilibrium state of T at temperature T. Statistical m echanics further identifies this state with the Gibbs canonical ensemb le associated with T. For simple models we prove that the above pictur e is correct, provided the equilibrium state of the environment R is i tself given by its canonical ensemble. In the quantum case we also obt ain an exact formula for the thermal relaxation time. (C) 1997 America n Institute of Physics.