On the mixing property for a class of states of relativistic quantum fields

Let ω be a factor state on the quasilocal algebra A of observables generated by a relativistic quantum field, which, in addition, satisfies certain regularity conditions [satisfied by ground states and the recently constructed thermal states of the P(φ)2 theory]. We prove that there exist space- and time-translation invariant states, some of which are arbitrarily close to ω in the weak * topology, for which the time evolution is weakly asymptotically Abelian.