Exact number conserving phase-space dynamics of the M-site Bose-Hubbard model
Abstract
The dynamics of M-site, N-particle Bose-Hubbard systems is described in quantum phase space constructed in terms of generalized SU(M) coherent states. These states have a special significance for these systems as they describe fully condensed states. Based on the differential algebra developed by Gilmore, we derive an explicit evolution equation for the (generalized) Husimi-(Q)- and Glauber-Sudarshan-(P)-distributions. Most remarkably, these evolution equations turn out to be second order differential equations where the second order terms scale as 1/N with the particle number. For large N the evolution reduces to a (classical) Liouvillian dynamics. The phase space approach thus provides a distinguished instrument to explore the mean-field many-particle crossover. In addition, the thermodynamic Bloch equation is analyzed using similar techniques.
Keywords
Cite
@article{arxiv.0802.1139,
title = {Exact number conserving phase-space dynamics of the M-site Bose-Hubbard model},
author = {F. Trimborn and D. Witthaut and H. J. Korsch},
journal= {arXiv preprint arXiv:0802.1139},
year = {2009}
}
Comments
11 pages, Revtex 4