a1 Department of Mathematics, University of Nottingham, Nottingham NG7 2RD
a2 Department of Mathematics, King's College, London WC2R 2LS
It has recently been shown [7, 8, 4] that Markov dilations of quantum dynamical semigroups may be constructed by solving corresponding quantum stochastic differential equations. These equations may be interpreted as describing the evolution of a quantum system with a singular coupling to a Boson reservoir, moreover, when solutions are combined with the free evolution of the reservoir, a reversible evolution results which may be interpreted as that of the system plus reservoir. It is the purpose of the present paper to characterize the above stochastic evolutions essentially by a condition of with respect to the free evolution.
(Received April 11 1986)