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Lettere al nuovo cimento della societa italiana di fisica/Lettere al nuovo cimento

Particle fluctuations in bose statistics

Harald Wergeland

Published Jan 1, 1969• 7 citations
Publisher
DOI
10.1007/bf02753692

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arXiv:cond-mat/9909157•Journal of Physics B Atomic Molecular and Optical Physics•Aug 3, 1999•27 citations
Summary form only given.We use quantum kinetic theory to calculate the steady-state and the fluctuations of a trapped Bose-Einstein condensate at finite temperature. We divide the system into two parts. The first part consists of the condensate particles. They are described quantum mechanically using the number-conserving Bogoliubov method that allows us to characterize the condensate by the number of condensed particles. The second part are the noncondensed particles. They are treated as a classical gas in thermal equilibrium. Using quantum kinetic theory we find a master equation for the reduced density operator of the Bose-Einstein condensate. We calculate the steady-state of the system and investigate the effect of one-, two- and three-particle losses on the condensate. Using linearized Ito equations we find expressions for the intensity fluctuations and the amplitude fluctuations in the condensate. The effect of the trap losses on the particle statistics is also studied. We then assume that the condensate particles are coherently pumped into an untrapped internal energy level and fall down in gravity. For this situation we derive the relation between the statistics of the trapped condensate particles and the statistics of the particles arriving at an atom detector positioned below the condensate.
The analytical probability distributions of the quasi-two-dimensional (quasi-2D) (and purely 2D) ideal and interacting Bose gases are investigated by using a canonical ensemble approach. Using the analytical probability distribution of the condensate, the statistical properties such as the mean occupation number and particle number fluctuations of the condensate are calculated. Research shows that there is a continuous crossover of the statistical properties from a quasi-2D to a purely 2D ideal gas or interacting gas. In contrast to the case of a 3D Bose gas, the interaction between atoms changes, in a deep way, the nature of the particle number fluctuations.
We derive exact thermodynamic identities relating the average number of condensed atoms and the root-mean-square fluctuations determined in different statistical ensembles for the weakly interacting Bose gas confined in a box. This is achieved by introducing the concept of auxiliary partition functions for model Hamiltonians that do conserve the total number of particles. Exploiting such thermodynamic identities, we provide the first, completely analytical prediction of the microcanonical particle number fluctuations in the weakly interacting Bose gas. Such fluctuations, as a function of the volume V of the box are found to behave normally, in contrast with the anomalous scaling behaviour V 4/3 of the fluctuations in the ideal Bose gas.