CEA-Saclay, Service de Physique Théorique
91191 Gif-sur-Yvette Cedex, France
I discuss the effect of repulsive interactions on the transition temperature of a homogeneous dilute Bose gas at fixed density. This provides an application to the nanokelvin scale of techniques mostly discussed in this workshop in connection with phenomena occuring at exceedingly large temperatures (typically to ). This problem has had a long and controversial history. Recently, using various techniques, we have been able to prove that the change in is proportional to the scattering length a. In order to calculate the propertionality coefficient, we recognize that the Hamiltonian of the system is a particular example of that of the general N vector model, for N =2, and we generalize the problem to arbitrary N. This generalization allows to calculate the coefficient of by carrying out an expansion in 1/N. The result at leading order in 1/N happens to be independent of N, for non-trivial reasons. Surprisingly this result is in remarkable agreement with the most recent numerical simulations.
This talk is based on the articles:
G. Baym, J.-P. Blaizot, M. Holzmann, F. Laloë, and D. Vautherin. Phys. Rev. Letters 83 (1999) 1703, cond-mat/9905430.
G. Baym, J.-P. Blaizot and J. Zinn-Justin, to be published in Eur. Phys. Letters, cond-mat/9907241.