Abstract

Introduction

Achievement of Bose-Einstein condensation in dilute gas by means of evaporative cooling has made headlines all over the world.

The theory, originally developed for homogeneous systems, has been quickly modified to account for the trapping potential. For the most part, however, it is a mean field theory at zero absolute temperature. The most interesting features of any finite size multiparticle system are those related to statistics, fluctuations and coherence and the way these properties depend on temperature. This special issue deals with these features.

The papers by Grossman and Holthaus and by Weiss and Wilkens discuss fluctuations of the number of condensed atoms of ideal Bose gas. They deal with different binding potentials and with varying dimensions. The quantity studied depends for finite systems on the choice of the statistical ensemble. While at the end it is up to experiment to determine which is the ensemble that most closely describes the condensate, we know for sure that it is not the widely used grand canonical ensemble, which leads to inordinately large fluctuations at zero temperature. So the authors work with much more difficult canonical and microcanonical ensembles.

The paper by Dodd et. al. takes-up the problem of spatial coherence of the condensate at finite temperature. The intensity-intensity correlation function is computed for the condensate. The authors stress that the lowest order correlation function, while sufficient for the discussion of the interference of two condensates is not characterizing the state of the quantum system uniquely.

Finally, the paper by You et. al. returns to the collective excitations of the condensate and reports a detailed analysis of the oscillation frequencies at high energies. The complex dependencies of these excitation energies brings us close to the notions of dynamical chaos. The role of chaotic motions in the dynamics of the Bose-Einstein condensate remains to be studied.

I am indebted to the authors of these papers, all of whom have been personally invited to contribute to this focus issue, for their high quality results written up at such a short notice.

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