Semiclassical quantization of the Bogoliubov spectrum

Details Semiclassical quantization of the Bogoliubov spectrum Semiclassical quantization of the Bogoliubov spectrum

2007-02-20

arxiv.org/abs/cond-mat/0702458v1

Phys. Rev. Lett. 99, 020401 (2007)

Physics

Condensed Matter

Statistical Mechanics

4.1 pages, 3 figures

Scientific paper

10.1103/PhysRevLett.99.020401

We analyze the Bogoliubov spectrum of the 3-sites Bose-Hubbard model with finite number of Bose particles by using a semiclassical approach. The Bogoliubov spectrum is shown to be associated with the low-energy regular component of the classical Hubbard model. We identify the full set of the integrals of motions of this regular component and, quantizing them, obtain the energy levels of the quantum system. The critical values of the energy, above which the regular Bogoliubov spectrum evolves into a chaotic spectrum, is indicated as well.

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