The master T-operator for the Gaudin model and the KP hierarchy
arXiv:1306.1111 · doi:10.1016/j.nuclphysb.2014.03.008
Abstract
Following the approach of [arXiv:1112.3310], we construct the master T -operator for the quantum Gaudin model with twisted boundary conditions and show that it satisfies the bilinear identity and Hirota equations for the classical KP hierarchy. We also characterize the class of solutions to the KP hierarchy that correspond to eigenvalues of the master T-operator and study dynamics of their zeros as functions of the spectral parameter. This implies a remarkable connection between the quantum Gaudin model and the classical Calogero-Moser system of particles.
56 pages, v2: details added in appendix C, v3: published version
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- On the classical r-matrix structure of the rational BC(n) Ruijsenaars-Schneider-van Diejen system
- Quantum-classical correspondence for gl(1|1) supersymmetric Gaudin magnet with boundary
- Integrable many-body systems of Calogero-Ruijsenaars type