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Discrete Thermodynamic Bethe Ansatz

Michel Bergere·Ken-Ichiro Imura·Stephane Ouvry
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Abstract

We propose discrete TBA equations for models with discrete spectrum. We illustrate our construction on the Calogero-Moser model and determine the discrete 2-body TBA function which yields the exact N-body Calogero-Moser thermodynamics. We apply this algorithm to the Lieb-Liniger model in a harmonic well, a model which is relevant for the microscopic description of harmonically trapped Bose-Einstein condensates in one dimension. We find that the discrete TBA reproduces correctly the N-body groundstate energy of the Lieb-Liniger model in a harmonic well at first order in perturbation theory, but corrections do appear at second order.

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Michel Bergere, Ken-Ichiro Imura, Stephane Ouvry. 2001-04-06. Discrete Thermodynamic Bethe Ansatz. https://doi.org/10.1016/s0550-3213(01)00271-1

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