arXiv:hep-th/0703124 · Journal of Statistical Mechanics Theory and Experiment

On the Bethe ansatz for the Jaynes–Cummings–Gaudin model

O. Babelon, Dmitry Valer'evich Talalaev

Published Jun 18, 2007• 72 citations

Abstract

We investigate the quantum Jaynes–Cummings model—a particular case of the Gaudin model with one of the spins being infinite. Starting from the Bethe equations we derive Baxter's equation and from it a closed set of equations for the eigenvalues of the commuting Hamiltonians. A scalar product in the separated variables representation is found for which the commuting Hamiltonians are Hermitian. In the semi-classical limit the Bethe roots accumulate on very specific curves in the complex plane. We give the equation for these curves. They build up a system of cuts modelling the spectral curve as a two-sheeted cover of the complex plane. Finally, we extend some of these results to the XXX Heisenberg spin chain.

DOI: 10.1088/1742-5468/2007/06/p06013

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