The Two-Site Bose–Hubbard Model |
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Authors: | Jon Links Angela Foerster Arlei Prestes Tonel Gilberto Santos |
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Affiliation: | 1. Centre for Mathematical Physics, School of Physical Sciences, The University of Queensland, Queensland, 4072, Australia 2. Instituto de Física da UFRGS, Av. Bento Gon?alves 9500, Porto Alegre, RS, Brazil
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Abstract: | The two-site Bose–Hubbard model is a simple model used to study Josephson tunneling between two Bose–Einstein condensates. In this work we give an overview of some mathematical aspects of this model. Using a classical analysis, we study the equations of motion and the level curves of the Hamiltonian. Then, the quantum dynamics of the model is investigated using direct diagonalization of the Hamiltonian. In both of these analyses, the existence of a threshold coupling between a delocalized and a self-trapped phase is evident, in qualitative agreement with experiments. Communicated by Vincent Rivasseau This work is dedicated to the memory of Daniel Arnaudon Submitted: January 30, 2006; Accepted: June 6, 2006 |
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