RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor
Guidelines for authors
Publishing Ethics

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



CMFD:
Year:
Volume:
Issue:
Page:
Find






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


CMFD, 2013, Volume 48, Pages 93–110 (Mi cmfd242)  

This article is cited in 1 scientific paper (total in 1 paper)

On dynamical properties of a one-parameter family of transformations arising in averaging of semigroups

V. Sakbaev

MIPT, Department of Higher Mathematics, Dolgoprudny, Moscow region, Russia

Abstract: To describe the dynamics of quantum systems with degenerate symmetric but not self-adjoint Hamiltonian, we consider the Naimark extension of the Hamiltonian to a self-adjoint operator in an extended Hilbert space. We relate to the symmetric Hamiltonian a one-parameter family of averaged dynamical transformations of the set of quantum states obtained from a unitary group of transformations of the extended Hilbert space by using a conditional expected value to an algebra of bounded operators acting in the original space. We establish the absence of the semigroup property and injectivity of the family of averaged dynamical transformations. We obtain a representation of trajectories of the averaged family of dynamical transformations by maximum points of functionals on the space of mappings of the time interval into the set of quantum states.

Full text: PDF file (367 kB)
References: PDF file   HTML file

English version:
Journal of Mathematical Sciences, 2014, 202:6, 869–886

UDC: 517.946+517.98

Citation: V. Sakbaev, “On dynamical properties of a one-parameter family of transformations arising in averaging of semigroups”, Proceedings of the Sixth International Conference on Differential and Functional-Differential Equations (Moscow, August 14–21, 2011). Part 4, CMFD, 48, PFUR, M., 2013, 93–110; Journal of Mathematical Sciences, 202:6 (2014), 869–886

Citation in format AMSBIB
\Bibitem{Sak13}
\by V.~Sakbaev
\paper On dynamical properties of a~one-parameter family of transformations arising in averaging of semigroups
\inbook Proceedings of the Sixth International Conference on Differential and Functional-Differential Equations (Moscow, August 14--21, 2011). Part~4
\serial CMFD
\yr 2013
\vol 48
\pages 93--110
\publ PFUR
\publaddr M.
\mathnet{http://mi.mathnet.ru/cmfd242}
\transl
\jour Journal of Mathematical Sciences
\yr 2014
\vol 202
\issue 6
\pages 869--886
\crossref{https://doi.org/10.1007/s10958-014-2083-9}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84921936626}


Linking options:
  • http://mi.mathnet.ru/eng/cmfd242
  • http://mi.mathnet.ru/eng/cmfd/v48/p93

    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. I. V. Volovich, V. Zh. Sakbaev, “On quantum dynamics on $C^*$-algebras”, Proc. Steklov Inst. Math., 301 (2018), 25–38  mathnet  crossref  crossref  isi  elib  elib
  • Современная математика. Фундаментальные направления
    Number of views:
    This page:250
    Full text:85
    References:30

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019