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Matematicheskie Zametki, 1997, Volume 61, Issue 4, Pages 612–622
DOI: https://doi.org/10.4213/mzm1539
(Mi mzm1539)
 

This article is cited in 29 scientific papers (total in 29 papers)

The quantum stochastic equation is unitarily equivalent to a symmetric boundary value problem for the Schrödinger equation

A. M. Chebotarev

M. V. Lomonosov Moscow State University, Faculty of Physics
References:
Abstract: We prove that the solution of the Hudson–Parthasarathy quantum stochastic differential equation in the Fock space coincides with the solution of a symmetric boundary value problem for the Schrödinger equation in the interaction representation generated by the energy operator of the environment. The boundary conditions describe the jumps in the phase and the amplitude of the Fourier transforms of the Fock vector components as any of its arguments changes the sign. The corresponding Markov evolution equation (the Lindblad equation or the “master equation”) is derived from the boundary value problem for the Schrödinger equation.
Received: 11.12.1996
English version:
Mathematical Notes, 1997, Volume 61, Issue 4, Pages 510–518
DOI: https://doi.org/10.1007/BF02354995
Bibliographic databases:
UDC: 519.217
Language: Russian
Citation: A. M. Chebotarev, “The quantum stochastic equation is unitarily equivalent to a symmetric boundary value problem for the Schrödinger equation”, Mat. Zametki, 61:4 (1997), 612–622; Math. Notes, 61:4 (1997), 510–518
Citation in format AMSBIB
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\by A.~M.~Chebotarev
\paper The quantum stochastic equation is unitarily equivalent to a~symmetric boundary value problem for the Schr\"odinger equation
\jour Mat. Zametki
\yr 1997
\vol 61
\issue 4
\pages 612--622
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\crossref{https://doi.org/10.4213/mzm1539}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1620012}
\zmath{https://zbmath.org/?q=an:0919.60093}
\transl
\jour Math. Notes
\yr 1997
\vol 61
\issue 4
\pages 510--518
\crossref{https://doi.org/10.1007/BF02354995}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1997XR25700034}
Linking options:
  • https://www.mathnet.ru/eng/mzm1539
  • https://doi.org/10.4213/mzm1539
  • https://www.mathnet.ru/eng/mzm/v61/i4/p612
  • This publication is cited in the following 29 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математические заметки Mathematical Notes
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    References:85
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