Bethe Ansatz Solutions of the Bose-Hubbard Dimer

Details Bethe Ansatz Solutions of the Bose-Hubbard Dimer Bethe Ansatz Solutions of the Bose-Hubbard Dimer

2006-12-29

arxiv.org/abs/nlin/0612063v1

SIGMA 2 (2006), 095, 8 pages

Nonlinear Sciences

Exactly Solvable and Integrable Systems

This is a contribution to the Vadim Kuznetsov Memorial Issue on Integrable Systems and Related Topics, published in SIGMA (Sym

Scientific paper

10.3842/SIGMA.2006.095

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.

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