Non-skew-symmetric classical r-matrices, algebraic Bethe ansatz, and Bardeen-Cooper-Schrieffer-type integrable systems
- International School for Advanced Studies, via Beirut 2-4, 34014 Trieste (Italy) and Bogoliubov Institute for Theoretical Physics, Metrologichna St. 14-b, Kiev 03143 (Ukraine)
We construct quantum integrable systems associated with non-skew-symmetric gl(2)-valued classical r-matrices. We find a new explicit multiparametric family of such the non-skew-symmetric classical r-matrices. We consider two classes of examples of the corresponding integrable systems, namely generalized Gaudin systems with and without an external magnetic field. In the case of arbitrary r-matrices diagonal in a standard gl(2)-basis, we calculate the spectrum of the corresponding quantum integrable systems using the algebraic Bethe ansatz. We apply these results to a construction of integrable fermionic models and obtain a wide class of integrable Bardeen-Cooper-Schrieffer (BCS)-type fermionic Hamiltonians containing the pairing and electrostatic interaction terms. We also consider special cases when the corresponding integrable Hamiltonians contain only pairing interaction term and are exact analogs of the 'reduced BCS Hamiltonian' of Richardson.
- OSTI ID:
- 21176074
- Journal Information:
- Journal of Mathematical Physics, Vol. 50, Issue 3; Other Information: DOI: 10.1063/1.3072912; (c) 2009 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
- Country of Publication:
- United States
- Language:
- English
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