Dilation of a class of quantum dynamical semigroups

Goswami, Debashish ; Sinha, Kalyan B. (2007) Dilation of a class of quantum dynamical semigroups Communications on Stochastic Analysis, 1 (1). pp. 87-101. ISSN 0973-9599

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Hudson-Parthasarathy (H-P) type quantum stochastic dilation of a class of C0 semigroups of completely positive maps (quantum dynamical or Markov semigroups) on a von Neumann or C* algebra, with unbounded generators, is constructed under some assumptions on the semigroup and its generator. The assumption of symmetry with respect to a semifinite trace allows the use of Hilbert space techniques,while that of covariance with respect to an action of a Lie group on the algebra gives a better control on the domain of the generator. A dilation of the dynamical semigroup is obtained, under some further assumptions on the domain of the generator, with the help of a conjugation by a unitary quantum stochastic process satisfying Hudson-Parthasarathy equation in Fock space.

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