RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Mat. Zametki:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Mat. Zametki, 2003, Volume 74, Issue 5, Pages 762–781 (Mi mz297)  

This article is cited in 4 scientific papers (total in 4 papers)

On the Strong Resolvent Convergence of the Schrödinger Evolution to Quantum Stochastics

A. M. Chebotareva, G. V. Ryzhakovb

a M. V. Lomonosov Moscow State University, Faculty of Physics
b M. V. Lomonosov Moscow State University

Abstract: For a class of Hamiltonians including a model of the quantum detector of gravitational waves, we prove the strong convergence of the Schrödinger evolution to quantum stochastics. We show that the strong resolvent limit of a sequence of self-adjoint Hamiltonians is a symmetric boundary-value problem in Fock space, and the limit evolution of the partial trace with respect to the mixed state cannot be described by a unique equation of Lindblad type. On the contrary, each component of the mixed state generates a proper evolution law.

DOI: https://doi.org/10.4213/mzm297

Full text: PDF file (319 kB)
References: PDF file   HTML file

English version:
Mathematical Notes, 2003, 74:5, 717–733

Bibliographic databases:

UDC: 517.958
Received: 13.12.2002
Revised: 06.07.2003

Citation: A. M. Chebotarev, G. V. Ryzhakov, “On the Strong Resolvent Convergence of the Schrödinger Evolution to Quantum Stochastics”, Mat. Zametki, 74:5 (2003), 762–781; Math. Notes, 74:5 (2003), 717–733

Citation in format AMSBIB
\Bibitem{CheRyz03}
\by A.~M.~Chebotarev, G.~V.~Ryzhakov
\paper On the Strong Resolvent Convergence of the Schr\"odinger Evolution to Quantum Stochastics
\jour Mat. Zametki
\yr 2003
\vol 74
\issue 5
\pages 762--781
\mathnet{http://mi.mathnet.ru/mz297}
\crossref{https://doi.org/10.4213/mzm297}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2042835}
\zmath{https://zbmath.org/?q=an:1115.81046}
\transl
\jour Math. Notes
\yr 2003
\vol 74
\issue 5
\pages 717--733
\crossref{https://doi.org/10.1023/B:MATN.0000009005.56775.7c}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000187966900013}


Linking options:
  • http://mi.mathnet.ru/eng/mz297
  • https://doi.org/10.4213/mzm297
  • http://mi.mathnet.ru/eng/mz/v74/i5/p762

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Ryzhakov G. V., “Asymptotic solutions of the quantum stochastic Liouville equation for an oscillator with regard to dissipation”, Russ. J. Math. Phys., 12:3 (2005), 386–393  mathscinet  zmath  isi  elib
    2. G. V. Ryzhakov, “Resolvent limits of the quantum evolution of open systems”, Math. Notes, 80:3 (2006), 454–458  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    3. Derezinski J. De Roeck W., “Reduced and Extended Weak Coupling Limit”, Noncommutative Harmonic Analysis with Applications to Probability, Banach Center Publications, 78, ed. Bozejko M. Krystek A. Mlotkowski W. Wysoczanski J., Panstwowe Wydawnictwo Naukowe Polish Sci Publ, 2007, 91–119  crossref  mathscinet  isi
    4. Bouten L., Van Handel R., “Discrete approximation of quantum stochastic models”, J. Math. Phys., 49:10 (2008), 102109, 19 pp.  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
  • Математические заметки Mathematical Notes
    Number of views:
    This page:333
    Full text:137
    References:36
    First page:3

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020