Abstract
We give a self-contained, tutorial review of recent works on the statistics of the number of particles contained in a Bose-Einstein condensate within the canonical ensemble, both for ideal and weakly interacting Bose gases. While in the case of the ideal gas there exists a general mathematical framework for computing the fluctuation of the condensate particles in any trap, the analysis of the weakly interacting case is restricted to a homogeneous gas in the framework of the Bogoliubov theory. In particular, we present a simplified derivation of the pair characteristic function which governs the condensate statistics, first obtained by Kocharovsky, Kocharovsky, and Scully [Physical Review A 61, 053606 (2000)].
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
For a review, see W. Ketterle, D.S. Durfee, D.M. Stamper-Kurn: ‘Making, Probing and Understanding Bose-Einstein Condensates’. In: Proceedings of the International. School of Physics “Enrico Fermi”, Course CXL, ed. by M. Inguscio, S. Stringari, and C.E. Wiemann (IOS Press, Amsterdam, 1999), pp. 67–176
M. Wilkens, F. Illuminati, M. Krämer: J. Phys. B 33, L779 (2000), and references therein
R.M. Ziff, G.E. Uhlenbeck, M. Kac: Phys. Rep. 32, 169 (1977)
S. Grossmann, M. Holthaus: Phys. Rev. E 54, 3495 (1996)
H.D. Politzer: Phys. Rev. A 54, 5048 (1996)
C. Weiss, M. Wilkens: Opt. Express 1, 272 (1997)
P. Navez, D. Bitouk, M. Gajda, Z. Idziaszek, K. Rzażewski: Phys. Rev. Lett. 79, 1789 (1997)
M. Holthaus, E. Kalinowski, K. Kirsten: Ann. Phys. (N.Y.) 270, 198 (1998)
M. O. Scully: Phys. Rev. Lett. 82, 3927 (1999)
V.V. Kocharovsky, M.O. Scully, S.-Y. Zhu, M.S. Zubairy: Phys. Rev. A 61, 023609 (2000)
S. Giorgini, L.P. Pitaevskii, S. Stringari: Phys. Rev. Lett. 80, 5040 (1998)
F. Meier, W. Zwerger: Phys. Rev. A 60, 5133 (1999)
V.V. Kocharovsky, Vl.V. Kocharovsky, M.O. Scully: Phys. Rev. Lett. 84, 2306 (2000)
V.V. Kocharovsky, Vl.V. Kocharovsky, M.O. Scully: Phys. Rev. A 61, 053606 (2000)
Z. Idziaszek, M. Gajda, P. Navez, M. Wilkens, K. Rzażewski: Phys. Rev. Lett. 82, 4376 (1999)
F. Illuminati, P. Navez, M. Wilkens: J. Phys. B 32, L461 (1999)
M. Holthaus, K.T. Kapale, V.V. Kocharovsky, M.O. Scully: Physica A 300, 433 (2001)
L.D. Landau, E.M. Lifshitz: Course of Theoretical Physics, Vol. 9: Statistical. Physics, Part 2 (Butterworth-Heinemann, Oxford, 1998)
L.D. Landau, E.M. Lifshitz: Course of Theoretical Physics, Vol. 5: Statistical. Physics, Part 1 (Butterworth-Heinemann, Oxford, 2001)
K. Huang: Statistical Mechanics (John Wiley, New York, 1963)
R.K. Pathria: Statistical Mechanics (Pergamon Press, Oxford, 1985)
M. Fierz: Helv. Phys. Acta 29, 47 (1956)
Handbook of Mathematical Functions, ed. by M. Abramowitz and I.A. Stegun (Dover, New York, 1972)
C.W. Gardiner: Handbook of Stochastic Methods (Springer Verlag, Berlin, 1985)
K. Kirsten, D.J. Toms: Phys. Rev. E 59, 158 (1999)
A. Voros: Commun. Math. Phys. 110, 439 (1987)
E.T. Whittaker, G.N. Watson: A Course of Modern Analysis (Cambridge University Press, Cambridge, 1969)
S.R. de Groot, G.J. Hooyman, C.A. ten Seldam: Proc. Roy. Soc. London A 203, 266 (1950)
V. Bagnato, D.E. Pritchard, D. Kleppner: Phys. Rev. A 35, 4354 (1987)
M. Holthaus, K.T. Kapale, M.O. Scully: Phys. Rev. E 65, 036129 (2002)
N. Bogoliubov: J. Phys. USSR 11, 23 (1947)
T.D. Lee, C.N. Yang: Phys. Rev. 105, 1119 (1957)
T.D. Lee, K. Huang, C.N. Yang: Phys. Rev. 106, 1135 (1957)
R.A. Ferell, N. Meynhard, H. Schmidt, F. Schwabl, P. Szépfalusy: Ann. Phys. (N.Y.) 47, 565 (1968)
R. Graham: Phys. Rev. Lett. 81, 5256 (1998)
R. Graham: Phys. Rev. A 62, 023609 (2000)
C. Weiss, M. Holthaus: Europhys. Lett., to appear (2002)
F.T. Arecchi, E. Courtens, R. Gilmore, H. Thomas: Phys. Rev. A 6, 2211 (1972)
J. Schwinger: In Quantum Theory of Angular Momentum, ed. by L.C. Biedenharn and H. van Dam (Academic, New York, 1965)
B.L. Schumaker, C.M. Caves: Phys. Rev. A 31, 3093 (1985)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Boers, D., Holthaus, M. (2002). Canonical Statistics of Occupation Numbers for Ideal and Weakly Interacting Bose-Einstein Condensates. In: Dauxois, T., Ruffo, S., Arimondo, E., Wilkens, M. (eds) Dynamics and Thermodynamics of Systems with Long-Range Interactions. Lecture Notes in Physics, vol 602. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45835-2_11
Download citation
DOI: https://doi.org/10.1007/3-540-45835-2_11
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-44315-5
Online ISBN: 978-3-540-45835-7
eBook Packages: Springer Book Archive