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Fluctuations in the Bose Gas with Attractive Boundary Conditions
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Preprint-KUL-TF-2001/22
Fluctuations in the Bose Gas with Attractive
Boundary Conditions
J. Lauwers1, A. Verbeure2
Instituut voor Theoretische Fysica, Katholieke Universiteit Leuven,
Celestijnenlaan 200D, B-3001 Leuven, Belgium
November 2001
Abstract
In this paper limiting distribution functions of field and density fluctuations are ex-
plicitly and rigorously computed for the different phases of the Bose gas. Several
Gaussian and non-Gaussian distribution functions are obtained and the dependence
on boundary conditions is explicitly derived. The model under consideration is the
free Bose gas subjected to attractive boundary conditions, such boundary conditions
yield a gap in the spectrum. The presence of a spectral gap and the method of the
coupled thermodynamic limits are the new aspects of this work, leading to new scal-
ing exponents and new fluctuation distribution functions.
Keywords
Quantum Fluctuations, Distribution Functions, Bose-Einstein Condensation, Bound-
ary Conditions.
1Bursaal KUL FLOF-10408
1Email: joris.lauwers@fys.kuleuven.ac.be
2Email: andre.verbeure@fys.kuleuven.ac.be
1 Introduction
Normal and critical fluctuations in the ideal Bose gas with Dirichlet or periodic boundary
conditions are explicitly studied at different levels of rigour in [1–10]. Condensation occurs
only at dimensions ν ≥ 3. It turns out that the behaviour of the energy gap of the finite
volume spectrum as a function of the volume is determining for the degree of abnormality
of the fluctuations in the condensate regime. Typical is that the limit spectrum has no
energy gap. The ideal Bose gas with attractive boundary conditions [11, 12] on the other
hand is quite different in nature. Condensation is possible in all space dimensions, and the
spectrum has a finite energy gap in the thermodynamic limit. In this paper we analyse
the nature of field and density fluctuations for the Bose gas with attractive boundary
c
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