On the theory of ideal Bose-gas

Ideal Bose-gas with finite particle number N is investigated. It is shown that the well-known Bose–Einstein distribution of particles over their quantum states consists of two terms — Bose–Einstein term and an additional N-dependent one. The statement that the chemical potential of the ideal Bose-gas should be negative requires tobe also corrected. It is obtained that the analytically calculated observables rather slowly approach the thermodynamic limit following the law N^–1/3lnN.

Key words: Bose-distribution, Bose–Einstein condensation, condensate density, critical temperature.

References

1. L. D. Landau and E. M. Lifshitz, Statistical Physics (Pergamon Press, New York, 1980). Google Scholar

2. K. Huang, Statistical Mechanics (Wiley, New York, 1987). Google Scholar

3. A. Isihara, Statistical Physics (Acad. Press, New York, 1971). Google Scholar

4. A. Einstein, Sitzungsber. K. Preuss Acad. Wiss. Phys. Math. Kl, 261 (1924). Google Scholar

5. K. B. Davis, M.-O. Mewes, M. R. Andrews, N. J. van Druten, D. S. Durfee, M. Kurn, and W. Ketterle, Phys. Rev. Lett. 75, 3969 (1995). CrossRef Google Scholar

6. M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Wieman, and E. A. Cornell, Science 269, 198 (1995). CrossRef Google Scholar

7. G. A. Melkov, V. L. Safonov, A. Y. Taranenko, and S. V. Sholom, J. Magn. Magn. Mater. 132, 180 (1994). CrossRef Google Scholar

8. A. I. Bugrij and V. M. Loktev, Fiz. Nizk. Temp. 33, 51 (2007) [Low Temp. Phys. 33, 37 (2007)]. CrossRef Google Scholar

9. A. I. Bugrij and V. M. Loktev, Fiz. Nizk. Temp. 39, 1333 (2013) [Low Temp. Phys. 39, 1037 (2013)]. CrossRef Google Scholar

10. V. B. Timofeev, A. V. Gorbunov, and D. A. Demin, Fiz. Nizk. Temp. 37, 229 (2011) [Low Temp. Phys. 37, 179 (2011)]. CrossRef Google Scholar

11. J. P. Einstein and A. H. McDonald, Nature 432, 691 (2004). CrossRef Google Scholar

12. A. Kagar, M. S. Rak, S. Vig, A. A. Husain, F. Ficker, Y. Joe, L. Venema, G. J. MacDougall, T. C. Chiang, F. Fradkin, J. van Wezel, and P. A. Abramonte, Science 358, 1314 (2018). CrossRef Google Scholar

13. V. B. Timofeev, Fiz. Tekhn. Polupr. 46, 865 (2012). Google Scholar

14. J. Kasprzak, M. Richard, S. Kundermann, A. Baas, J. M. J. Keeling, F. V. Marchetti, M. H. Szymanska, R. Andre, J. L. Staehli, V. Savona, P. B. Littlewood, B. Deveaud, and L S Dang, Nature 443, 409 (2006). CrossRef Google Scholar

15. F. P. Laussy, I. Shelykh, A. V. Kavokin, and G. Malpuech, Phys. Rev. B 73, 035315 (2006). CrossRef Google Scholar

16. S. A. Moskalenko and D. W. Snoke, BoseâEinstein Conden-Sation of Excitons and Biexcitons (Cambridge Univ. Press, Cambridge, 2000). Google Scholar

17. L. M. Satarov, I. N. Mishustin, A. Motornenko, V. Vovchenko, and M. I. Gorenstein, Phys. Rev. C 99, 024909 (2019). CrossRef Google Scholar