We present the construction of completely positive semigroups on the von Neumann algebra B(h) of all bounded operators on a complex separable Hilbert space h with a given form generator and their dilations to homomorphic inner flows via Hudson-Parthasarathy quantum stochastic differential equations. We discuss concrete examples emphasizing non conservativity issues of the minimal semigroup that could end up in a type II product system of the minimal dilation.
Quantum Markov Semigroups and Flows Arising from Form Generators on B(h)
FAGNOLA, FRANCO
2009-01-01
Abstract
We present the construction of completely positive semigroups on the von Neumann algebra B(h) of all bounded operators on a complex separable Hilbert space h with a given form generator and their dilations to homomorphic inner flows via Hudson-Parthasarathy quantum stochastic differential equations. We discuss concrete examples emphasizing non conservativity issues of the minimal semigroup that could end up in a type II product system of the minimal dilation.File in questo prodotto:
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