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Steklov Institute of Mathematics at St.Petersburg

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PREPRINT 09/2003

N. M. Bogoliubov, R. K. Bullough, C. Malyshev, J. Timonen
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FINITE-TEMPERATURE CORRELATIONS
IN THE ONE-DIMENSIONAL TRAPPED
AND UNTRAPPED BOSE GASES:
FUNCTIONAL INTEGRAL APPROACH

This preprint was accepted July 7, 2003

ABSTRACT:
We calculate the dynamic single-particle and many-particle
correlation functions at nonzero temperature in
one-dimensional trapped repulsive Bose gases. The decay for
increasing distance between the points of these correlation
functions is governed by a scaling exponent that has a
universal expression in terms of observed quantities. This
expression is valid in the weak-interaction
Gross--Pitaevskii as well as in the strong-interaction
Girardeau-Tonks limit, but the observed quantities involved
depend on the interaction strength. The confining trap
introduces a weak center-of-mass dependence in the scaling
exponent. We also conjecture results for the
density-density correlation function.

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