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

This article is cited in 6 scientific papers (total in 6 papers)

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:

Received: 16.11.2000

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
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\paper Metric Properties of Bogoliubov Trajectories in Statistical Equilibrium Theory
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\jour Theoret. and Math. Phys.
\yr 2001
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\issue 1
\pages 513--527
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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  mathnet  mathscinet  zmath
    2. V. R. Fatalov, “Some asymptotic formulas for the Bogoliubov Gaussian measure”, Theoret. and Math. Phys., 157:2 (2008), 1606–1625  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    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  mathnet  crossref  crossref  adsnasa  isi
    4. V. R. Fatalov, “Laplace-type exact asymptotic formulas for the Bogoliubov Gaussian measure”, Theoret. and Math. Phys., 168:2 (2011), 1112–1149  mathnet  crossref  crossref  mathscinet  adsnasa  isi
    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  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  elib
    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  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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