On the Bose-Éinstein condensation of a perfect gas

Jeffrey Olafsen

This chapter focuses on integrating the distribution function over all the states of conserved Bosons to obtain a relation between particle density and the chemical potential. It describes the phenomenon of Bose-Einstein condensation in a perfect boson gas. The chapter discusses the experimental observation of Bose-Einstein condensation in perfect gases. There are two routes to obtaining Bose-Einstein condensation in a perfect gas. One is to reduce the mass of the particle, thus reducing critical density to a low value at a reasonable temperature. The other route is to lower the temperature to the point where the critical density is so low that the particles are too far apart to interact with each other.

Lawrence J. Landau, Ivan F. Wilde

Otto Halpern

Joseph V. Pulé, Valentin Anatol'evich Zagrebnov

We study the problem of Bose–Einstein condensation in the perfect Bose gas in the canonical ensemble, in anisotropically dilated rectangular parallelepipeds (Casimir boxes). We prove that in the canonical ensemble for these anisotropic boxes there is the same type of generalized Bose–Einstein condensation as in the grand-canonical ensemble for the equivalent geometry. However the amount of condensate in the individual states is different in some cases and so are the fluctuations.

Fabrice P. Laussy

Thomas Jaeck, Joseph V. Pulé, Valentin Anatol'evich Zagrebnov

We study the perfect Bose gas in random external potentials and show that there is generalized Bose-Einstein condensation in the random eigenstates if and only if the same occurs in the one-particle kinetic-energy eigenstates, which corresponds to the generalized condensation of the free Bose gas. Moreover, we prove that the amounts of both condensate densities are equal. Our method is based on the derivation of an explicit formula for the occupation measure in the one-body kinetic-energy eigenstates which describes the repartition of particles among these non-random states. This technique can be adapted to re-examine the properties of the perfect Bose gas in the presence of weak (scaled) non-random potentials, for which we establish similar results.