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arXiv · 0802.1139

Exact number conserving phase-space dynamics of the M-site Bose-Hubbard model

F. Trimborn·D. Witthaut·H. J. Korsch
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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.

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F. Trimborn, D. Witthaut, H. J. Korsch. 2008-02-08. Exact number conserving phase-space dynamics of the M-site Bose-Hubbard model. https://doi.org/10.1103/physreva.77.043631

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