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 ℋ 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 ℋ 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 ℋ 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.
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Spehner, D., Bellissard, J. A Kinetic Model of Quantum Jumps. Journal of Statistical Physics 104, 525–572 (2001). https://doi.org/10.1023/A:1010320520088
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DOI: https://doi.org/10.1023/A:1010320520088