• Title, Summary, Keyword: quantum stochastic process

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RECONSTRUCTION THEOREM FOR STATIONARY MONOTONE QUANTUM MARKOV PROCESSES

  • Heo, Jae-Seong;Belavkin, Viacheslav P.;Ji, Un Cig
    • Bulletin of the Korean Mathematical Society
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    • v.49 no.1
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    • pp.63-74
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    • 2012
  • Based on the Hilbert $C^*$-module structure we study the reconstruction theorem for stationary monotone quantum Markov processes from quantum dynamical semigroups. We prove that the quantum stochastic monotone process constructed from a covariant quantum dynamical semigroup is again covariant in the strong sense.

A FRESNEL TYPE CLASS ON FUNCTION SPACE

  • Chang, Seung-Jun;Choi, Jae-Gil;Lee, Sang-Deok
    • The Pure and Applied Mathematics
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    • v.16 no.1
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    • pp.107-119
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    • 2009
  • In this paper we define a Banach algebra on very general function space induced by a generalized Brownian motion process rather than on Wiener space, but the Banach algebra can be considered as a generalization of Fresnel class defined on Wiener space. We then show that several interesting functions in quantum mechanic are elements of the class.

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