In this article we make a brief review of the generalized Gaudin spin chains with [21] and without [18], [19] external magnetic field in the simplest case of g=so(3) and provide the r-matrix interpretation and generalization of the recent results of [38], [39], [40], on their exact solution. We present the classification theorem for the r-matrices that are diagonal in the natural basis and for the “shift elements” playing the role of the interaction strengths and external magnetic fields in the corresponding Gaudin-type models. We apply these results to the description, classification and solution of BCS-Richardson-type models. In particular, we introduce “elliptic” BCS-Richardson hamiltonian corresponding to non-skew-symmetric elliptic r-matrix and calculate its spectrum. We show that the “closed” [23], [30] and the “open” [36] BCS-Richardson hamiltonian of p+ip-type coincide with its trigonometric degenerations.

Skrypnyk, T. (2019). Classical r-matrices, “elliptic” BCS and Gaudin-type hamiltonians and spectral problem. NUCLEAR PHYSICS. B, 941, 225-248 [10.1016/j.nuclphysb.2019.02.018].

Classical r-matrices, “elliptic” BCS and Gaudin-type hamiltonians and spectral problem

Skrypnyk, T.
Primo
2019

Abstract

In this article we make a brief review of the generalized Gaudin spin chains with [21] and without [18], [19] external magnetic field in the simplest case of g=so(3) and provide the r-matrix interpretation and generalization of the recent results of [38], [39], [40], on their exact solution. We present the classification theorem for the r-matrices that are diagonal in the natural basis and for the “shift elements” playing the role of the interaction strengths and external magnetic fields in the corresponding Gaudin-type models. We apply these results to the description, classification and solution of BCS-Richardson-type models. In particular, we introduce “elliptic” BCS-Richardson hamiltonian corresponding to non-skew-symmetric elliptic r-matrix and calculate its spectrum. We show that the “closed” [23], [30] and the “open” [36] BCS-Richardson hamiltonian of p+ip-type coincide with its trigonometric degenerations.
Articolo in rivista - Articolo scientifico
Nuclear and High Energy Physics
English
2019
941
225
248
none
Skrypnyk, T. (2019). Classical r-matrices, “elliptic” BCS and Gaudin-type hamiltonians and spectral problem. NUCLEAR PHYSICS. B, 941, 225-248 [10.1016/j.nuclphysb.2019.02.018].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/227420
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