After discussing the key idea underlying the Maxwell’s Demon ensemble, we employ this idea for calculating fluctuations of ideal Bose gas condensates in traps with power-law single-particle energy spectra. Two essentially different cases have to be distinguished. If the heat capacity remains continuous at the condensation point in the large-N-limit, the fluctuations of the number of condensate particles vanish linearly with temperature, independent of the trap characteristics. If the heat capacity becomes discontinuous, the fluctuations vanish algebraically with temperature, with an exponent determined by the trap. Our results are based on an integral representation that yields the solution to both the canonical and the microcanonical fluctuation problem in a singularly transparent manner.

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1. L.D. Landau and E.M. Lifshitz, Statistical Physics (Pergamon, London, 1959).
2. R.K. Pathria, Statistical Mechanics (Pergamon, Oxford, 1985).
3. I. Fujiwara, D. ter Haar, and H. Wergeland, "Fluctuations in the population of the ground state of Bose systems", J. Stat. Phys. 2, 329-346 (1970). [CrossRef]
4. R.M. Zi, G.E. Uhlenbeck, and M. Kac, "The ideal Bose-Einstein gas, revisited", Phys. Rep. 32, 169-248 (1977). [CrossRef]
5. M.H. Anderson, J.R. Ensher, M.R. Matthews, C.E. Wieman, and E.A. Cornell, "Observation of Bose-Einstein condensation in a dilute atomic vapor", Science 269, 198-201 (1995). [CrossRef]
6. K.B. Davis, M.-O. Mewes, M.R. Andrews, N.J. van Druten, D.S. Durfee, D.M. Kurn, and W. Ketterle, "Bose-Einstein condensation in a gas of sodium atoms", Phys. Rev. Lett. 75, 3969-3973 (1995). [CrossRef] [PubMed]
7. C.C. Bradley, C.A. Sackett, and R.G. Hulet, "Bose-Einstein condensation of lithium: observation of limited condensate number", Phys. Rev. Lett. 78, 985-989 (1997). [CrossRef] [PubMed]
8. W. Ketterle and N.J. van Druten, "Bose-Einstein condensation of a finite number of particles trapped in one or three dimensions", Phys. Rev. A 54, 656-660 (1996). [CrossRef]
9. N.J. van Druten and W. Ketterle, "Two-step condensation of the ideal Bose gas in highly anisotropic traps", Phys. Rev. Lett. 79, 549-552 (1997). [CrossRef] [PubMed]
10. S. Grossmann and M. Holthaus, "Microcanonical uctuations of a Bose system's ground state occupation number", Phys. Rev. E 54, 3495-3498 (1996). [CrossRef]
11. S. Grossmann and M. Holthaus, "From number theory to statistical mechanics: Bose-Einstein condensation in isolated traps" (Preprint, Marburg, 1997). [CrossRef]
12. M. Wilkens, "From Chinese wok to Mexican hat: Bose-Einstein condensation in an isolated Bose gas" (Preprint, Konstanz, 1996).
13. P. Navez, D. Bitouk, M. Gajda, Z. Idziaszek, and K. Rzazewski, "The fourth statistical ensemble
14. S. Grossmann and M. Holthaus, "Fluctuations of the particle number in a trapped Bose condensate" (Preprint, Marburg, 1997). [CrossRef]
15. P. Borrmann and G. Franke, "Recursion formulas for quantum statistical partition functions", J. Chem. Phys. 98, 2484-2485 (1993). [CrossRef]
16. B. Eckhardt, "Eigenvalue statistics in quantum ideal gases" (Preprint, Oldenburg, 1997). [CrossRef]
17. M. Wilkens and C. Weiss, "Universality classes and particle number uctuations of trapped ideal Bose gases" (Preprint, Potsdam, 1997).
18. S.R. de Groot, G.J. Hooyman, and C.A. ten Seldam, "On the Bose-Einstein condensation", Proc. Roy. Soc. London A 203, 266-286 (1950).
19. M. Gajda and K. Rzazewski, "Fluctuations of Bose-Einstein condensate", Phys. Rev. Lett. 78, 2686-2689 (1997). See Eq. (13) therein. [CrossRef]
20. J.E. Robinson, "Note on the Bose-Einstein integral functions", Phys. Rev. 83, 678-679 (1951). See also Ref. [2], Appendix D.
21. F.Y. Wu, G. Rollet, H.Y. Huang, J.M. Maillard, C.-K. Hu, and C.-N. Chen, "Directed compact lattice animals, restricted partitions of an integer, and the in finite-states Potts model", Phys. Rev. Lett. 76, 173-176 (1996). [CrossRef] [PubMed]

Other

• L.D. Landau and E.M. Lifshitz, Statistical Physics (Pergamon, London, 1959).
• R.K. Pathria, Statistical Mechanics (Pergamon, Oxford, 1985).
• I. Fujiwara, D. ter Haar, and H. Wergeland, "Fluctuations in the population of the ground state of Bose systems", J. Stat. Phys. 2, 329-346 (1970). [CrossRef]
• R.M. Zi, G.E. Uhlenbeck, and M. Kac, "The ideal Bose-Einstein gas, revisited", Phys. Rep. 32, 169-248 (1977). [CrossRef]
• M.H. Anderson, J.R. Ensher, M.R. Matthews, C.E. Wieman, and E.A. Cornell, "Observation of Bose-Einstein condensation in a dilute atomic vapor", Science 269, 198-201 (1995). [CrossRef]
• K.B. Davis, M.-O. Mewes, M.R. Andrews, N.J. van Druten, D.S. Durfee, D.M. Kurn, and W. Ketterle, "Bose-Einstein condensation in a gas of sodium atoms", Phys. Rev. Lett. 75, 3969-3973 (1995). [CrossRef] [PubMed]
• C.C. Bradley, C.A. Sackett, and R.G. Hulet, "Bose-Einstein condensation of lithium: observation of limited condensate number", Phys. Rev. Lett. 78, 985-989 (1997). [CrossRef] [PubMed]
• W. Ketterle and N.J. van Druten, "Bose-Einstein condensation of a finite number of particles trapped in one or three dimensions", Phys. Rev. A 54, 656-660 (1996). [CrossRef]
• N.J. van Druten and W. Ketterle, "Two-step condensation of the ideal Bose gas in highly anisotropic traps", Phys. Rev. Lett. 79, 549-552 (1997). [CrossRef] [PubMed]
• S. Grossmann and M. Holthaus, "Microcanonical uctuations of a Bose system's ground state occupation number", Phys. Rev. E 54, 3495-3498 (1996). [CrossRef]
• S. Grossmann and M. Holthaus, "From number theory to statistical mechanics: Bose-Einstein condensation in isolated traps" (Preprint, Marburg, 1997). [CrossRef]
• M. Wilkens, "From Chinese wok to Mexican hat: Bose-Einstein condensation in an isolated Bose gas" (Preprint, Konstanz, 1996).
• P. Navez, D. Bitouk, M. Gajda, Z. Idziaszek, and K. Rzazewski, "The fourth statistical ensemble
• S. Grossmann and M. Holthaus, "Fluctuations of the particle number in a trapped Bose condensate" (Preprint, Marburg, 1997). [CrossRef]
• P. Borrmann and G. Franke, "Recursion formulas for quantum statistical partition functions", J. Chem. Phys. 98, 2484-2485 (1993). [CrossRef]
• B. Eckhardt, "Eigenvalue statistics in quantum ideal gases" (Preprint, Oldenburg, 1997). [CrossRef]
• M. Wilkens and C. Weiss, "Universality classes and particle number uctuations of trapped ideal Bose gases" (Preprint, Potsdam, 1997).
• S.R. de Groot, G.J. Hooyman, and C.A. ten Seldam, "On the Bose-Einstein condensation", Proc. Roy. Soc. London A 203, 266-286 (1950).
• M. Gajda and K. Rzazewski, "Fluctuations of Bose-Einstein condensate", Phys. Rev. Lett. 78, 2686-2689 (1997). See Eq. (13) therein. [CrossRef]
• J.E. Robinson, "Note on the Bose-Einstein integral functions", Phys. Rev. 83, 678-679 (1951). See also Ref. [2], Appendix D.
• F.Y. Wu, G. Rollet, H.Y. Huang, J.M. Maillard, C.-K. Hu, and C.-N. Chen, "Directed compact lattice animals, restricted partitions of an integer, and the in finite-states Potts model", Phys. Rev. Lett. 76, 173-176 (1996). [CrossRef] [PubMed]

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