Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)


SIGMA 2 (2006), 095, 8 pages      nlin.SI/0612063      http://dx.doi.org/10.3842/SIGMA.2006.095
Contribution to the Vadim Kuznetsov Memorial Issue

Bethe Ansatz Solutions of the Bose-Hubbard Dimer

Jon Links and Katrina E. Hibberd
Centre for Mathematical Physics, School of Physical Sciences, The University of Queensland, 4072, Australia

Received October 26, 2006, in final form December 19, 2006; Published online December 29, 2006

Abstract
The Bose-Hubbard dimer Hamiltonian is a simple yet effective model for describing tunneling phenomena of Bose-Einstein condensates. One of the significant mathematical properties of the model is that it can be exactly solved by Bethe ansatz methods. Here we review the known exact solutions, highlighting the contributions of V.B. Kuznetsov to this field. Two of the exact solutions arise in the context of the Quantum Inverse Scattering Method, while the third solution uses a differential operator realisation of the su(2) Lie algebra.

Key words: Bose-Hubbard dimer; Bethe ansatz.

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