Trapped one-dimensional Bose gas as a Luttinger liquid

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Abstract
The low-energy fluctuations of a trapped, interacting quasi-one-dimensional Bose gas are studied. Our considerations apply to experiments with highly anisotropic traps. We show that under suitable experimental conditions the system can be described as a Luttinger liquid. This implies that the correlation function of the bosons decays algebraically, preventing Bose-Einstein condensation. At significantly lower temperatures a finite-size gap destroys the Luttinger liquid picture and Bose-Einstein condensation is again possible.
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