RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
 General information Latest issue Forthcoming papers Archive Impact factor Guidelines for authors License agreement Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Trudy MIAN: Year: Volume: Issue: Page: Find

 Tr. Mat. Inst. Steklova, 2018, Volume 301, Pages 33–47 (Mi tm3904)

On quantum dynamics on $C^*$-algebras

I. V. Volovicha, V. Zh. Sakbaevb

a Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991 Russia
b Moscow Institute of Physics and Technology (State University), Institutskii per. 9, Dolgoprudnyi, Moscow oblast, 141701 Russia

Abstract: We consider the problem of constructing quantum dynamics for symmetric Hamiltonian operators that have no self-adjoint extensions. For an earlier studied model, it was found that an elliptic self-adjoint regularization of a symmetric Hamiltonian operator allows one to construct quantum dynamics for vector states on certain $C^*$-subalgebras of the algebra of bounded operators in a Hilbert space. In the present study, we prove that one can extend the dynamics to arbitrary states on these $C^*$-subalgebras while preserving the continuity and convexity. We show that the obtained extension of the dynamics of the set of states on $C^*$-subalgebras is the limit of a sequence of regularized dynamics under removal of the elliptic regularization. We also analyze the properties of the limit dynamics of the set of states on the $C^*$-subalgebras.

 Funding Agency Grant Number Ministry of Education and Science of the Russian Federation 5-100 The second author was supported by the Moscow Institute of Physics and Technology within the Russian Academic Excellence Project 5-100.

DOI: https://doi.org/10.1134/S0371968518020036

Full text: PDF file (255 kB)
First page: PDF file
References: PDF file   HTML file

English version:
Proceedings of the Steklov Institute of Mathematics, 2018, 301, 25–38

Bibliographic databases:

Document Type: Article
UDC: 517.98

Citation: I. V. Volovich, V. Zh. Sakbaev, “On quantum dynamics on $C^*$-algebras”, Complex analysis, mathematical physics, and applications, Collected papers, Tr. Mat. Inst. Steklova, 301, MAIK Nauka/Interperiodica, Moscow, 2018, 33–47; Proc. Steklov Inst. Math., 301 (2018), 25–38

Citation in format AMSBIB
\Bibitem{VolSak18} \by I.~V.~Volovich, V.~Zh.~Sakbaev \paper On quantum dynamics on $C^*$-algebras \inbook Complex analysis, mathematical physics, and applications \bookinfo Collected papers \serial Tr. Mat. Inst. Steklova \yr 2018 \vol 301 \pages 33--47 \publ MAIK Nauka/Interperiodica \publaddr Moscow \mathnet{http://mi.mathnet.ru/tm3904} \crossref{https://doi.org/10.1134/S0371968518020036} \elib{http://elibrary.ru/item.asp?id=35246286} \transl \jour Proc. Steklov Inst. Math. \yr 2018 \vol 301 \pages 25--38 \crossref{https://doi.org/10.1134/S008154381804003X} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000442104600003} \elib{http://elibrary.ru/item.asp?id=35743423} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85051728633}