Darmstadt 2008 – scientific programme

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Q: Fachverband Quantenoptik und Photonik

Q 32: Quantengase (Gitter III)

Q 32.5: Talk

Thursday, March 13, 2008, 09:30–09:45, 1C

Exact phase-space dynamics of the M-site Bose-Hubbard model — •Friederike Trimborn, Dirk Witthaut, and Hans Jürgen Korsch — FB Physik, TU Kaiserslautern, 67663 Kaiserslautern

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 are equivalent to the 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) Liouvillean dynamics. The phase space approach thus provides a distinguished instrument to explore the mean-field many-particle crossover.