Abstract
The formalism of Ursell operators provides a self-consistent integral equation for the one-particle reduced operator. In three dimensions this technique yields values of the shift in the Bose-Einstein condensation (BEC) transition temperature, as a function of the scattering length, that are in good agreement with those of Green's function and quantum Monte Carlo methods. We have applied the same equations to a uniform two-dimensional system and find that, as we alter the chemical potential, an instability develops so that the self-consistent equations no longer have a solution. This instability, which seems to indicate that interactions restore a transition, occurs at a non-zero value of an effective chemical potential. The non-linear equations are limited to temperatures greater than or equal to Tc, so that they do not indicate the nature of the new stable state, but we speculate concerning whether it is a Kosterlitz-Thouless state or a “smeared” BEC, which might avoid any violation of the Hohenberg theorem, as described in an accompanying paper.
Similar content being viewed by others
REFERENCES
M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Wieman, and E. A. Cornell,Science 269, 198 (1995); K. B. Davis, M.-0._Mewes, M. R. Andrews, N.J. van Druten, D. S. Durfee, D. M. Kurn, and W. Ketterle, Phys. Rev. Lett. 75, 3969 (1995); C. C. Bradley, C. A. Sackett, J. J. Tollett, and R. G. Hulet, Phys. Rev. Lett. 75, 1687 (1995).
F. Dalfovo, S. Giorgini, L. Pitaevskii, and S. Stringari, Rev. Mod.Phys. 71, 463 (1999).
M. Holzmann, P. Grüter, and F. Laloë, Europhys. Journ.B 10,739 (1999).
G. Baym, J.-P. Blaizot, M. Holzmann, F. Laloë, and D. Vautherin, Phys. Rev.Lett. 83, 1703 (1999).
G. Baym, J.-P. Blaizot, and J. Zinn-Justin, Europhys. Lett. 49,150 (2000).
P. Grüter and F. Laloë, J. Phys. I France 5, 181 (1995); 5, 1255 (1995);P. Grüter, F. Laloë, A. E. Meyerovich, and W. Mullin, J. Phys. I France 7, 485 (1997); F. Laloe, in Bose-Einstein Condensation, edited by A. Griffin, D. W. Snoke, and S. Stringari, Cambridge Univ. Press (1995).
M.Holzmann and W. Krauth, Phys. Rev. Lett. 83, 2687 (1999).
J. M. Kosterlitz and D. J. Thouless, J. Phys. C 6, 1181 (1973); V. L. Berezinskii, Sou. Phys. JETP 32, 493 (1971).
P.C. Hohenberg, Phys. Rev. 158, 383 (1967).
W. J. Mullin, M. Holzmann, and F.Laloë, (This conference).
V. N. Popov, Functional Integrals in Quantum FieldTheory and Statistical Physics, (Reidel Publishing Company, Dordrecht, 1983).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Mullin, W.J., Holzmann, M. & Laloë, F. Instability in a Two-Dimensional Dilute Interacting Bose System. Journal of Low Temperature Physics 121, 269–274 (2000). https://doi.org/10.1023/A:1017560521078
Issue Date:
DOI: https://doi.org/10.1023/A:1017560521078