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 TMF, 2001, Volume 127, Number 1, Pages 125–142 (Mi tmf452)

Metric Properties of Bogoliubov Trajectories in Statistical Equilibrium Theory

D. P. Sankovich

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: We investigate some properties of the Bogoliubov measure that appear in statistical equilibrium theory for quantum systems and establish the nondifferentiability of the Bogoliubov trajectories in the corresponding function space. We prove a theorem on the quadratic variation of trajectories and study the properties implied by this theorem for the scale transformations. We construct some examples of semigroups related to the Bogoliubov measure. Independent increments are found for this measure. We consider the relation between the Bogoliubov measure and parabolic partial differential equations.

DOI: https://doi.org/10.4213/tmf452

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English version:
Theoretical and Mathematical Physics, 2001, 127:1, 513–527

Bibliographic databases:

Citation: D. P. Sankovich, “Metric Properties of Bogoliubov Trajectories in Statistical Equilibrium Theory”, TMF, 127:1 (2001), 125–142; Theoret. and Math. Phys., 127:1 (2001), 513–527

Citation in format AMSBIB
\Bibitem{San01} \by D.~P.~Sankovich \paper Metric Properties of Bogoliubov Trajectories in Statistical Equilibrium Theory \jour TMF \yr 2001 \vol 127 \issue 1 \pages 125--142 \mathnet{http://mi.mathnet.ru/tmf452} \crossref{https://doi.org/10.4213/tmf452} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1863523} \zmath{https://zbmath.org/?q=an:0993.82005} \transl \jour Theoret. and Math. Phys. \yr 2001 \vol 127 \issue 1 \pages 513--527 \crossref{https://doi.org/10.1023/A:1010368009861} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000170446000009} 

• http://mi.mathnet.ru/eng/tmf452
• https://doi.org/10.4213/tmf452
• http://mi.mathnet.ru/eng/tmf/v127/i1/p125

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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. D. P. Sankovich, “The Bogolyubov Functional Integral”, Proc. Steklov Inst. Math., 251 (2005), 213–245
2. V. R. Fatalov, “Some asymptotic formulas for the Bogoliubov Gaussian measure”, Theoret. and Math. Phys., 157:2 (2008), 1606–1625
3. R. S. Pusev, “Asymptotics of small deviations of the Bogoliubov processes with respect to a quadratic norm”, Theoret. and Math. Phys., 165:1 (2010), 1348–1357
4. V. R. Fatalov, “Laplace-type exact asymptotic formulas for the Bogoliubov Gaussian measure”, Theoret. and Math. Phys., 168:2 (2011), 1112–1149
5. V. R. Fatalov, “Asymptotic behavior of small deviations for Bogoliubov's Gaussian measure in the $L^p$ norm, $2\le p\le\infty$”, Theoret. and Math. Phys., 173:3 (2012), 1720–1733
6. V. R. Fatalov, “Exact Laplace-type asymptotic formulas for the Bogoliubov Gaussian measure: The set of minimum points of the action functional”, Theoret. and Math. Phys., 191:3 (2017), 870–885
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