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Integrability of the pairing hamiltonian

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arxiv nucl-th/9708031 v1 pith:RNJVJZNA submitted 1997-08-18 nucl-th chao-dynnlin.CDnlin.SIsolv-int

M.C. Cambiaggio , A.M.F. Rivas , M. Saraceno This is my paper
classification nucl-thchao-dynnlin.CDnlin.SIsolv-int
keywords operatorspairinghamiltonianintegrablelevelbogoliubovcharacterclassical
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We show that a many-body Hamiltonian that corresponds to a system of fermions interacting through a pairing force is an integrable problem, i.e. it has as many constants of the motion as degrees of freedom. At the classical level this implies that the Time-dependent Hartree-Fock- Bogoliubov dynamics is integrable and at the quantum level that there are conserved operators of two-body character which reduce to the number operators when the pairing strength vanishes. We display these operators explicitly and study in detail the three-level example.

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