Abstract
In this paper limiting distribution functions of field and density fluctuations are explicitly 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 scaling exponents and new fluctuation distribution functions.
Similar content being viewed by others
REFERENCES
W. F. Wreszinski, Fluctuations in some mean-field models in quantum statistics, Helv. Phys. Acta 46:844–868 (1974).
R. M. Ziff, G. E. Uhlenbeck, and M. Kac, The ideal Bose gas, revisited, Phys. Rep. 32:169–248 (1977).
E. Buffet and J. V. Pulè, Fluctuation properties of the imperfect Bose gas, J. Math. Phys. 24:1608–1616 (1983).
M. Fannes, P. Martin, and A. Verbeure, On the equipartition law in quantum statistical mechanics, J. Phys. A: Math. Gen. 6:4293–4306 (1983).
B. Nachtergaele, Quantum angular-momentum fluctuations, J. Math. Phys. 26:2317–2323 (1985).
P. Tuyls, M. Van Canneyt, and A. Verbeure, Angular-momentum fluctuations of the ideal Bose-gas in a rotating bucket, J. Phys. A: Math. Gen. 28:1–18 (1995).
M. Broidioi and A. Verbeure, Scaling behaviour in the Bose gas, Commun. Math. Phys. 174:635–660 (1996).
N. Angelescu, J. G. Brankov, and A. Verbeure, General one-particle fluctuations of the ideal Bose gas, J. Phys. A: Math. Gen. 29:3341–3356 (1996).
T. Michoel and A. Verbeure, Goldstone boson normal coordinates in interacting Bose gases, J. Stat. Phys. 96:1125–1162 (1999).
V. A. Zagrebnov and J.-B. Bru, The Bogoliubov model of weakly imperfect Bose gas, Phys. Rep. 350:291–434 (2001).
Derek W. Robinson, Bose-Einstein condensation with attractive boundary conditions, Commun. Math. Phys. 50:53–59 (1976).
L. J. Landau and I. F. Wilde, On the Bose-Einstein condensation of an ideal gas, Commun. Math. Phys. 70:43–51 (1979).
A. Verbeure and V. A. Zagrebnov, Gaussian, non-Gaussian critical fluctuations in the Curie-Weiss model, J. Stat. Phys. 75:1137–1152 (1994).
D. W. Robinson, The Thermodynamic Pressure in Quantum Statistical Mechanics, Lecture Notes in Physics, Vol. 9 (Springer-Verlag, Berlin, 1971).
O. Bratteli and D. W. Robinson, Operator Algebras and Quantum Statistical Mechanics 2 (Springer-Verlag, Berlin, 1996).
W. Magnus, F. Oberhettinger, and R. P. Soni, Formulas and Theorems for the Special Functions of Mathematical Physics (Springer-Verlag, Berlin, 1966).
F. Papangelou, On the Gaussian flucutations of the critical Curie-Weiss model in statistical mechanics, Probability Theory Related Fields, 83:265–278 (1989).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Lauwers, J., Verbeure, A. Fluctuations in the Bose Gas with Attractive Boundary Conditions. Journal of Statistical Physics 108, 123–168 (2002). https://doi.org/10.1023/A:1015491519127
Issue Date:
DOI: https://doi.org/10.1023/A:1015491519127