Discrete thermodynamic Bethe ansatz

We propose discrete TBA equations for models with discrete spectrum. We ill ustrate our construction on the Calogero-Moser model and determine the disc rete 2-body TBA function which yields the exact N-body Calogero-Moser therm odynamics. We apply this algorithm to the Lieb-Liniger model in a harmonic well, a model which is relevant for the microscopic description of harmonic ally trapped Bose-Einstein condensates in one dimension. We find that the d iscrete TBA reproduces the N-body groundstate energy of the Lieb-Liniger mo del in a harmonic well at first order in perturbation theory, but correctio ns do appear at second order. (C) 2001 Elsevier Science B.V. All rights res erved.