Abstract
An E_0-semigroup acting on B(H) is called pure if the intersection of the ranges
α
t
(B(H))
,
t>0
, is the algebra of scalars. We determine all pure E_0-semigroups which have a weakly continuous invariant state
ω
and which are minimal in an appropriate sense. In such cases, for every normal state
ρ
there is convergence to equilibrium in the trace norm
lim
t→∞
∥ρ∘
α
t
−ω∥=0.
A normal state
ω
with this property is called an absorbing state. Such E_0-semigroups mest be cocycle perturbations of CAR/CCR flows, and we develop systematic methods for constructing those perturbations which have absorbing states with prescribed finite eigenvalue lists.