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Zap. Nauchn. Sem. POMI, 2007, Volume 347, Pages 56–74
(Mi znsl73)
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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 Received: 02.06.2006
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}
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http://mi.mathnet.ru/eng/znsl73 http://mi.mathnet.ru/eng/znsl/v347/p56
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