Abstract

A new class of models describing the dissipative dynamics of an open quantum system S by means of random time evolutions of pure states in its Hilbert space ? is considered. The random evolutions are linear and defined by Poisson processes. At the random Poissonian times, the wavefunction experiences discontinuous changes (quantum jumps). These changes are implemented by some non-unitary linear operators satisfying a locality condition. If the Hilbert space ? of S is infinite dimensional, the models involve an infinite number of independent Poisson processes and the total frequency of jumps may be infinite. We show that the random evolutions in ? are then given by some almost-surely defined unbounded random evolution operators obtained by a limit procedure. The average evolution of the observables of S is given by a quantum dynamical semigroup, its generator having the Lindblad form.(1) The relevance of the models in the field of electronic transport in Anderson insulators is emphasised.