RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
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



TMF:
Year:
Volume:
Issue:
Page:
Find






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


TMF, 1980, Volume 42, Number 1, Pages 101–111 (Mi tmf3726)  

This article is cited in 2 scientific papers (total in 2 papers)

Cauchy problem for stochastic Liouville equation with randomly variable Hamiltonian of perturbations in the form of a bounded operator

Yu. N. Barabanenkov


Abstract: A class of stochastic problems is considered, in which the perturbation hamiltoniarn of dynamic system depends on a random function of time and coordinates (“the potential”). It is assumed that the perturbation hamiltonian is a bounded operator for sufficiently regular realisations of the potential. The condition for the random potential to belong to the measurable real Hilbert space with finite measure as well as the property of potential correlations weakening is formulated in terms of cumulant functions. For the class of problems under consideration, the solution of the stochastic Liouville–Neumann equation is constructed and limiting theorem about the validity of basic kinetic equation is proved, which includes the approximation of weak interaction with external system and the approximation of small density.

Full text: PDF file (1486 kB)
References: PDF file   HTML file

English version:
Theoretical and Mathematical Physics, 1980, 42:1, 66–73

Bibliographic databases:

Received: 26.09.1978

Citation: Yu. N. Barabanenkov, “Cauchy problem for stochastic Liouville equation with randomly variable Hamiltonian of perturbations in the form of a bounded operator”, TMF, 42:1 (1980), 101–111; Theoret. and Math. Phys., 42:1 (1980), 66–73

Citation in format AMSBIB
\Bibitem{Bar80}
\by Yu.~N.~Barabanenkov
\paper Cauchy problem for stochastic Liouville equation with randomly variable Hamiltonian of~perturbations in~the form of~a~bounded operator
\jour TMF
\yr 1980
\vol 42
\issue 1
\pages 101--111
\mathnet{http://mi.mathnet.ru/tmf3726}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=561006}
\zmath{https://zbmath.org/?q=an:0419.60065|0434.60071}
\transl
\jour Theoret. and Math. Phys.
\yr 1980
\vol 42
\issue 1
\pages 66--73
\crossref{https://doi.org/10.1007/BF01019262}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1980KA96200011}


Linking options:
  • http://mi.mathnet.ru/eng/tmf3726
  • http://mi.mathnet.ru/eng/tmf/v42/i1/p101

    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. Yu. N. Barabanenkov, “Asymptotic method in the theory of the passage of fast charged particles through matter”, Theoret. and Math. Phys., 47:2 (1981), 442–449  mathnet  crossref  mathscinet  isi
    2. R. V. Bobrik, “Hierarchies of moment equations for the solution of the Schrödinger equation with random potential and their closure”, Theoret. and Math. Phys., 68:2 (1986), 841–847  mathnet  crossref  mathscinet  zmath  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
    Number of views:
    This page:239
    Full text:139
    References:29
    First page:1

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2021