On the structure of Markov flows

Details On the structure of Markov flows On the structure of Markov flows

1999-11-17

arxiv.org/abs/quant-ph/9911078v2

Physics

Quantum Physics

22 pages, LaTeX 2.09, proof of Lemma 23 corrected

Scientific paper

A new infinitesimal characterization of completely positive but not necessarily homomorphic Markov flows from a C^*-algebra to bounded operators on the boson Fock space over L^2(R) is given. Contrarily to previous characterizations, based on stochastic differential equations, this characterization is universal, i.e. valid for arbitrary Markov flows. With this result the study of Markov flows is reduced to the study of four C_0-semigroups. This includes the classical case and even in this case it seems to be new. The result is applied to deduce a new existence theorem for Markov flows.

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