Simple criterion for the occurrence of Bose-Einstein condensation and the Meissner-Ochsenfeld effect

Klaus Kirsten; David J. Toms

doi:10.1103/PhysRevD.55.7797

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Simple criterion for the occurrence of Bose-Einstein condensation and the Meissner-Ochsenfeld effect

Klaus Kirsten

David J. Toms

Universität Leipzig, Institut für Theoretische Physik, Augustusplatz 10, 04109 Leipzig, Germany

Department of Physics, University of Newcastle Upon Tyne, Newcastle Upon Tyne NE1 7RU, United Kingdom

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Phys. Rev. D 55, 7797 – Published 15 June, 1997

DOI: https://doi.org/10.1103/PhysRevD.55.7797

Abstract

We examine the occurrence of Bose-Einstein condensation in both nonrelativistic and relativistic systems with no self-interactions in a general setting. A simple condition for the occurrence of Bose-Einstein condensation is given. We show that condensation can occur only if $q >~ 3$ , where $q$ is the dimension associated with the continuous part of the eigenvalue spectrum of the Hamiltonian for nonrelativistic systems or the spatial part of the Klein-Gordon operator for relativistic systems. Furthermore we show that the criterion for the appearance of the Meissner-Ochsenfeld effect is closely connected with that for the appearance of Bose-Einstein condensation.

References (50)

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S. Singh and R. K. Pathria, J. Phys. A 17, 2983 (1984).
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[c1] S. N. Bose, Z. Phys. 26, 178 (1924).

[c2] A. Einstein, Sitzungsber. K. Preuss. Akad. Wiss., Phys. Math. K1. 22, 261 (1924).

[c3] L. D. Landau and E. M. Lifshitz, Statistical Physics (Pergammon, London, 1969).

[c4] R. M. May, Phys. Rev. A 135, 1515 (1964).

[c5] J. I. Kapusta, Phys. Rev. D 24, 426 (1981).

[c6] H. E. Haber and H. A. Weldon, Phys. Rev. Lett. 46, 1497 (1981).

[c7] H. E. Haber and H. A. Weldon, Phys. Rev. D 25, 502 (1982).

[c8] K. Huang, in Bose-Einstein Condensation, edited by A. Griffin, D. W. Snoke, and S. Stringari (Cambridge University Press, Cambridge, England, 1995).

[c9] K. M. Benson, J. Bernstein, and S. Dodelson, Phys. Rev. D 44, 2480 (1991).

[c10] J. Bernstein and S. Dodelson, Phys. Rev. Lett. 66, 683 (1991).

[c11] K. Kirsten and D. J. Toms, Phys. Rev. D 51, 6886 (1995).

[c12] D. J. Toms, Phys. Rev. Lett. 69, 1152 (1992).

[c13] D. J. Toms, Phys. Rev. D 47, 2483 (1993).

[c14] M. B. Al’taie, J. Phys. A 11, 1603 (1978).

[c15] S. Singh and R. K. Pathria, J. Phys. A 17, 2983 (1984).

[c16] L. Parker and Y. Zhang, Phys. Rev. D 44, 2421 (1991).

[c17] G. Cognola and L. Vanzo, Phys. Rev. D 47, 4575 (1993).

[c18] J. S. Dowker and G. Kennedy, J. Phys. A 11, 895 (1978); J. S. Dowker and J. P. Schofield, Nucl. Phys. B327, 267 (1989).

[c19] A. A. Bytsenko, L. Vanzo, and S. Zerbini, Phys. Lett. B 291, 26 (1992).

[c20] K. Kirsten, Class. Quantum Grav. 8, 2239 (1991); J. Phys. A 24, 3281 (1991).

[c21] M. R. Schafroth, Helv. Phys. Acta 24, 645 (1951).

[c22] M. R. Schafroth, Phys. Rev. 100, 463 (1955).

[c23] R. M. May, Phys. Rev. 115, 254 (1959).

[c24] R. M. May, J. Math. Phys. (N.Y.) 6, 1462 (1965).

[c25] D. J. Toms, Phys. Rev. D 51, 1886 (1995).

[c26] D. J. Toms, Phys. Lett. B 343, 259 (1995).

[c27] J. Daicic, N. E. Frankel, and V. Kowalenko, Phys. Rev. Lett. 71, 1779 (1993).

[c28] J. Daicic, N. E. Frankel, R. M. Gallis, and V. Kowalenko, Phys. Rep. 237, 63 (1994).

[c29] P. Elmfors, D. Persson, and B. S. Skagerstam, Phys. Rev. Lett. 71, 480 (1993).

[c30] P. Elmfors, P. Liljenberg, D. Persson, and B. S. Skagerstam, Phys. Lett. B 348, 462 (1995).

[c31] J. Daicic and N. E. Frankel, Phys. Rev. D 53, 5745 (1996).

[c32] H. P. Rojas, Phys. Lett. B 379, 148 (1996).

[c33] K. Kirsten and D. J. Toms, Phys. Lett. B 368, 119 (1996).

[c34] K. Kirsten and D. J. Toms, Phys. Rev. A 54, 4188 (1996).

[c35] C. W. Bernard, Phys. Rev. D 9, 3312 (1974).

[c36] J. I. Kapusta, Finite Temperature Field Theory (Cambridge University Press, Cambridge, England, 1989).

[c37] N. P. Landsman and Ch. G. van Weert, Phys. Rep. 145, 141 (1987).

[c38] D. J. Toms, Phys. Rev. D 50, 6457 (1994).

[c39] B. S. DeWitt, Dynamical Theory of Groups and Fields (Gordon and Breach, New York, 1965).

[c40] S. W. Hawking, Commun. Math. Phys. 55, 133 (1977).

[c41] R. Critchley and J. S. Dowker, Phys. Rev. D 13, 3224 (1976).

[c42] D. J. Toms, Phys. Rev. B 50, 3120 (1994).

[c43] R. M. Ziff, G. E. Uhlenbeck, and M. Kac, Phys. Rep., Phys. Lett. 32C, 169 (1977).

[c44] J. D. Smith and D. J. Toms, Phys. Rev. D 53, 5771 (1996).

[c45] I. S. Gradshteyn and I. M. Ryzhik, Tables of Integrals, Series and Products (Academic, New York, 1965).

[c46] K. Kirsten and D. J. Toms (in preparation).

[c47] D. J. O’Connor, B. L. Hu, and T. C. Shen, Phys. Lett. B 130, 31 (1983); B. L. Hu and D. J. O’Connor, Phys. Rev. Lett. 56, 1613 (1986); Phys. Rev. D 36, 1701 (1987).

[c48] J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1962).

[c49] E. A. Guggenheim, Thermodynamics (North-Holland, Amsterdam, 1959).

[c50] S. S. Schweber, An Introduction to Relativistic Quantum Field Theory (Row, Peterson, Evanston, 1961).

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Simple criterion for the occurrence of Bose-Einstein condensation and the Meissner-Ochsenfeld effect

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