Dmitri Talalaev | Searcharxiv

arXiv2009

Manin Matrices, Quantum Elliptic Commutative Families and Characteristic Polynomial of Elliptic Gaudin Model

In this paper we construct the quantum spectral curve for the quantum dynamical elliptic gl(n) Gaudin model. We realize it considering a commutative family corresponding to the Felder's elliptic quantum group and taking the appropriate limit. The approach of Manin matrices here suits well to the problem of constructing the generation function of commuting elements which plays an important role in SoV and Langlands concept.

math-ph↗

arXiv2007

On the Bethe Ansatz for the Jaynes-Cummings-Gaudin model

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 of these curves. They build up a system of cuts modeling 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.

hep-th↗