Abstract
We demonstrate a method for finding the decoherence-subalgebra N(T) of a Gaussian quantum Markov semigroup on the von Neumann algebra B(Γ(C^d)) of all bounded operator on the Fock space Γ(C^d) on C^d. We show that N(T) is a type I von Neumann algebra L^∞(R^d_c;C)⊗B(Γ(C^d_f)) determined, up to unitary equivalence, by two natural numbers d_c,d_f≤ d. This result is illustrated by some applications and examples.