Markov dilations of nonconservative dynamical semigroups and a quantum boundary theory

B. V. Rajarama Bhat; K. R. Parthasarathy

Displaying similar documents to “Markov dilations of nonconservative dynamical semigroups and a quantum boundary theory”

Markov operators: applications to diffusion processes and population dynamics

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This note contains a survey of recent results concerning asymptotic properties of Markov operators and semigroups. Some biological and physical applications are given.

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W. Desch, W. Schappacher (1984)

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Veronica Umanità (2006)

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We define the transient and recurrent parts of a quantum Markov semigroup 𝓣 on a von Neumann algebra 𝓐 and we show that, when 𝓐 is σ-finite, we can write 𝓣 as the sum of such semigroups. Moreover, if 𝓣 is the countable direct sum of irreducible semigroups each with a unique faithful normal invariant state ρₙ, we find conditions under which any normal invariant state is a convex combination of ρₙ's.

A note on Howe's oscillator semigroup

Joachim Hilgert (1989)

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Analytic extensions of the metaplectic representation by integral operators of Gaussian type have been calculated in the $L^{2} (ℝ^{n})$ and the Bargmann-Fock realisations by Howe [How2] and Brunet-Kramer [Brunet-Kramer, Reports on Math. Phys., 17 (1980), 205-215]], respectively. In this paper we show that the resulting semigroups of operators are isomorphic and calculate the intertwining operator.

On a class of Markov type semigroups in spaces of uniformly continuous and bounded functions

Enrico Priola (1999)

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We study a new class of Markov type semigroups (not strongly continuous in general) in the space of all real, uniformly continuous and bounded functions on a separable metric space E. Our results allow us to characterize the generators of Markov transition semigroups in infinite dimensions such as the heat and the Ornstein-Uhlenbeck semigroups.

Stochastic Dynamics of Quantum Spin Systems

Adam Majewski, Robert Olkiewicz, Bogusław Zegarliński (1998)

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We show that recently introduced noncommutative $L_{p}$ -spaces can be used to constructions of Markov semigroups for quantum systems on a lattice.