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arXiv · 0802.1142

Beyond mean-field dynamics of small Bose-Hubbard systems based on the number-conserving phase space approach

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

The number-conserving quantum phase space description of the Bose-Hubbard model is discussed for the illustrative case of two and three modes, as well as the generalization of the two-mode case to an open quantum system. The phase-space description based on generalized SU(M) coherent states yields a Liouvillian flow in the macroscopic limit, which can be efficiently simulated using Monte Carlo methods even for large systems. We show that this description clearly goes beyond the common mean-field limit. In particular it resolves well-known problems where the common mean-field approach fails, like the description of dynamical instabilities and chaotic dynamics. Moreover, it provides a valuable tool for a semi-classical approximation of many interesting quantities, which depend on higher moments of the quantum state and are therefore not accessible within the common approach. As a prominent example, we analyse the depletion and heating of the condensate. A comparison to methods ignoring the fixed particle number shows that in this case artificial number fluctuations lead to ambiguities and large deviations even for quite simple examples.

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F. Trimborn, D. Witthaut, H. J. Korsch. 2008-10-28. Beyond mean-field dynamics of small Bose-Hubbard systems based on the number-conserving phase space approach. https://doi.org/10.1103/physreva.79.013608

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