Abstract
A Yukawa-like equation, introduced to evaluate the first order correlation function in a Bose-Einstein condensate, can be used to evaluate the atomic density fluctuations. It does not require a few mode approximation. We apply this approach to calculate the atomic fluctuations of a condensate of attractive atoms in a double-well potential. The atomic system undergoes a spatial symmetry breaking above a critical number ${N}_{c}$ of atoms. Near ${N}_{c}$ the atomic fluctuation $\ensuremath{\delta}N$ inside a single well becomes very large and experimentally observable by a phase-contrast imaging technique. $\ensuremath{\delta}N$ is related to the collective mode temperature, which may be different from the condensate temperature measured by means of the thermal tails. A one-dimensional array of wells is also considered.
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