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Mosc. Math. J., 2001, Volume 1, Number 3, Pages 307–313 (Mi mmj22)  

This article is cited in 4 scientific papers (total in 4 papers)

Euclidean Gibbs states of quantum crystals

S. A. Albeverioab, Yu. G. Kondrat'evcb, T. Pasurek, M. Röcknerb

a University of Bonn, Institute for Applied Mathematics
b Bielefeld University
c Institute of Mathematics, Ukrainian National Academy of Sciences

Abstract: We prove existence and uniform a priori estimates for Euclidean Gibbs states corresponding to quantum anharmonic crystals. Our method is based on a characterization of Gibbs measures in terms of their Radon–Nikodym derivatives with respect to local shifts of the configuration space and corresponding integration by parts formulas.

Key words and phrases: Quantum crystals, Euclidean Gibbs states, existence problem.

DOI: https://doi.org/10.17323/1609-4514-2001-1-3-307-313

Full text: http://www.ams.org/.../abst1-3-2001.html
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MSC: 82B10
Received: July 9, 2001; in revised form August 25, 2001
Language:

Citation: S. A. Albeverio, Yu. G. Kondrat'ev, T. Pasurek, M. Röckner, “Euclidean Gibbs states of quantum crystals”, Mosc. Math. J., 1:3 (2001), 307–313

Citation in format AMSBIB
\Bibitem{AlbKonPas01}
\by S.~A.~Albeverio, Yu.~G.~Kondrat'ev, T.~Pasurek, M.~R\"ockner
\paper Euclidean Gibbs states of quantum crystals
\jour Mosc. Math.~J.
\yr 2001
\vol 1
\issue 3
\pages 307--313
\mathnet{http://mi.mathnet.ru/mmj22}
\crossref{https://doi.org/10.17323/1609-4514-2001-1-3-307-313}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1877595}
\zmath{https://zbmath.org/?q=an:0993.82006}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000208587500001}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Albeverio S., Kondratiev Yu., Kozitsky Yu., Röckner M., “Small mass implies uniqueness of Gibbs states of a quantum crystal”, Comm. Math. Phys., 241:1 (2003), 69–90  crossref  mathscinet  zmath  adsnasa  isi
    2. Amour L., Cancelier C., Levy-Bruhl P., Nourrigat J., “States of a one dimensional quantum crystal”, C. R. Math. Acad. Sci. Paris, 336:12 (2003), 981–984  crossref  mathscinet  zmath  isi
    3. Albeverio S., Schachermayer W., Talagrand M., Lectures on probability theory and statistics, Lectures from the 30th Summer School on Probability Theory (Saint-Flour, August 17–September 3, 2000), Lecture Notes in Math., 1816, Springer-Verlag, Berlin, 2003, viii+291 pp.  crossref  mathscinet  zmath  isi
    4. Amour L., Cancelier C., Lévy-Bruhl P., Nourrigat J., “Decay of quantum correlations on a lattice by heat kernel methods”, Ann. Henri Poincaré, 8:8 (2007), 1469–1506  crossref  mathscinet  zmath  adsnasa  isi
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