Bose-Hubbard dimers, Viviani's windows and pendulum dynamics
Quantum Physics
2014-03-05 v3
Abstract
The two-mode Bose-Hubbard model in the mean-field approximation is revisited emphasizing a geometric interpretation where the system orbits appear as intersection curves of a (Bloch) sphere and a cylinder oriented parallel to the mode axis, which provide a generalization of Viviani's curve studied already in 1692. In addition, the dynamics is shown to agree with the simple mathematical pendulum. The areas enclosed by the generalised Viviani curves, the action integrals, which can be used to semiclassically quantize the N-particle eigenstates, are evaluated. Furthermore the significance of the original Viviani curve for the quantum system is demonstrated.
Cite
@article{arxiv.1308.3569,
title = {Bose-Hubbard dimers, Viviani's windows and pendulum dynamics},
author = {Eva-Maria Graefe and Hans Jürgen Korsch and Martin P. Strzys},
journal= {arXiv preprint arXiv:1308.3569},
year = {2014}
}
Comments
18 pages, 9 figures