A Bethe ansatz solvable model for superpositions of Cooper pairs and condensed molecular bosons

Hibberd, Katrina E. and Dunning, Clare and Links, Jon (2006) A Bethe ansatz solvable model for superpositions of Cooper pairs and condensed molecular bosons. Nuclear Physics B, 748 (3). pp. 458-472. ISSN 0550-3213. (doi:10.1016/j.nuclphysb.2006.04.026) (Full text available)

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We introduce a general Hamiltonian describing coherent superpositions of Cooper pairs and condensed molecular bosons. For particular choices of the coupling parameters, the model is integrable. One integrable manifold, as well as the Bethe ansatz solution, was found by Dukelsky et al. [J. Dukelsky, G.G. Dussel, C. Esebbag, S. Pittel, Phys. Rev. Lett. 93 (2004) 050403]. Here we show that there is a second integrable manifold, established using the boundary quantum inverse scattering method. In this manner we obtain the exact solution by means of the algebraic Bethe ansatz. In the case where the Cooper pair energies are degenerate we examine the relationship between the spectrum of these integrable Hamiltonians and the quasi-exactly solvable spectrum of particular Schrodinger operators. For the solution we derive here the potential of the Schrodinger operator is given in terms of hyperbolic functions. For the solution derived by Dukelsky et al., loc. cit. the potential is sextic and the wavefunctions obey PT-symmetric boundary conditions. This latter case provides a novel example of an integrable Hermitian Hamiltonian acting on a Fock space whose states map into a Hilbert space of PE-symmetric wavefunctions defined on a contour in the complex plane.

Item Type: Article
Subjects: Q Science > QA Mathematics (inc Computing science)
Divisions: Faculties > Sciences > School of Mathematics Statistics and Actuarial Science > Applied Mathematics
Depositing User: Clare Dunning
Date Deposited: 01 Sep 2008 13:40 UTC
Last Modified: 16 Jun 2014 11:52 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/4708 (The current URI for this page, for reference purposes)
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