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A Bethe ansatz solvable model for superpositions of Cooper pairs and condensed molecular bosons
Hibberd, K. E., Dunning, C. and Links, J. (2006) A Bethe ansatz solvable model for superpositions of Cooper pairs and condensed molecular bosons. Nuclear Physics B, 748 3: 458-472.
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| Author(s) |
Hibberd, K. E.
Dunning, C.
Links, J.
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| Title |
A Bethe ansatz solvable model for superpositions of Cooper pairs and condensed molecular bosons
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| Journal name |
Nuclear Physics B
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| Publication date |
2006
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| Volume number |
748
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| Issue number |
3
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| ISSN |
0550-3213
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| Start page |
458
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| End page |
472
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| Total pages |
15
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| Editor(s) |
Altarelli, G.
Bartel. W.
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| Place of publication |
Netherlands
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| Publisher |
Elsevier
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| Collection year |
2006
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| Subject |
C1
230199 Mathematics not elsewhere classified
240200 Theoretical and Condensed Matter Physics
230105 Group Theory And Generalisations (Incl. Topological Groups And Lie Groups)
780101 Mathematical sciences
010502 Integrable Systems (Classical and Quantum)
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| Abstract |
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. (c) 2006 Elsevier B.V. All rights reserved.
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| Keyword(s) |
Physics, Particles & Fields
Symmetric Quantum-mechanics
Bose-einstein Condensate
Reflection Equation
Systems
Hamiltonians
Potentials
Algebras
Boundary
Spectra
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