Return to equilibrium

The problem of return to equilibrium is phrased in terms of aC*-algebraU, and two one-parameter groups of automorphisms , ^P corresponding to the unperturbed and locally perturbed evolutions. The asymptotic evolution, under , of ^P -invariant, and ^P -K.M.S., states is considered. This study is a generalization of scattering theory and results concerning the existence of limit states are obtained by techniques similar to those used to prove the existence, and intertwining properties, of wave-operators. Conditions of asymptotic abelianness provide the necessary dispersive properties for the return to equilibrium. It is demonstrated that the ^P -equilibrium states and their limit states are coupled by automorphisms with a quasi-local property; they are not necessarily normal with respect to one another. An application to theX–Y model is given which extends previously known results and other applications, and examples, are given for the Fermi gas.