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SIGMA 2 (2006), 095, 8 pages nlin.SI/0612063
https://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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