A kinetic model of quantum jumps

A new class of models describing the dissipative dynamics of an open quantu m system S by means of random time evolutions of pure states in its Hilbert space H is considered. The random evolutions are linear and defined by Poi sson processes. At the random Poissonian times. the wavefunction experience s discontinuous changes (quantum jumps). These changes are implemented by s ome nonunitary linear operators satisfying a locality condition. If the Hil bert space H of S is infinite dimensional, the models involve an infinite n umber of independent Poisson processes and the total frequency of jumps may be infinite. We show that the random evolutions in H are then given by som e 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 Anders on insulators is emphasised.