2008/02/08 by F. Trimborn, Dirk Witthaut, D. Witthaut +1
Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Nonlinear Photonic Systems #Strong Light-Matter Interactions #quant-ph
paper · pdf · doi:10.1103/physreva.77.043631
published as Phys. Rev. A 77, 043631 (2008) · 11 pages, Revtex 4
arxiv created 2008/02/08 · openalex publication_date 2008/04/25 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
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.