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 Zap. Nauchn. Sem. POMI, 2007, Volume 347, Pages 56–74 (Mi znsl73)

On the calculation of the asymptotics of the two-point correlation function of the one-dimensional Bose gas in the trapping potential

N. M. Bogolyubov, K. L. Malyshev

St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences

Abstract: The quantum field-theoretical model, which describes spatially non-homogeneous one-dimensional repulsive Bose gas in an external harmonic potential is considered. The two-point correlation function is calculated in the framework of the functional integration. The corresponding functional integrals are estimated by means of the stationary phase approximation. The asymptotical estimates are obtained in the limit when the temperature is going to zero while the volume occupied by the quasi-condensate is increased. The power-law behavior is found for the correlation function in this limit. It is demonstrated that the power-law behavior is governed by the critical exponent dependent on the spatial arguments.

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English version:
Journal of Mathematical Sciences (New York), 2008, 151:2, 2829–2839

Bibliographic databases:

UDC: 517.9

Citation: N. M. Bogolyubov, K. L. Malyshev, “On the calculation of the asymptotics of the two-point correlation function of the one-dimensional Bose gas in the trapping potential”, Questions of quantum field theory and statistical physics. Part 20, Zap. Nauchn. Sem. POMI, 347, POMI, St. Petersburg, 2007, 56–74; J. Math. Sci. (N. Y.), 151:2 (2008), 2829–2839

Citation in format AMSBIB
\Bibitem{BogMal07} \by N.~M.~Bogolyubov, K.~L.~Malyshev \paper On the calculation of the asymptotics of the two-point correlation function of the one-dimensional Bose gas in the trapping potential \inbook Questions of quantum field theory and statistical physics. Part~20 \serial Zap. Nauchn. Sem. POMI \yr 2007 \vol 347 \pages 56--74 \publ POMI \publaddr St.~Petersburg \mathnet{http://mi.mathnet.ru/znsl73} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2458884} \transl \jour J. Math. Sci. (N. Y.) \yr 2008 \vol 151 \issue 2 \pages 2829--2839 \crossref{https://doi.org/10.1007/s10958-008-9001-y} \scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-49249121899}