2009/06/12 by Jiao Wang, Jiangbin Gong
Mathematics · Physics and Astronomy · #Butterfly #Cold Atom Physics and Bose-Einstein Condensates #Floquet theory #Fractal #Mathematical analysis #Mathematical physics #Mathematics #Nonlinear system #Physics #Quantum #Quantum chaos and dynamical systems #Quantum mechanics #Quantum, superfluid, helium dynamics #Spectrum (functional analysis) #cond-mat.other #nlin.CD #quant-ph
paper · pdf · doi:10.1103/physreve.81.026204
published as Phys. Rev. E 81, 026204 (2010) · 11 pages, 9 figures, relatively large size, a full-length report of the findings in arXiv 0906.2259
arxiv created 2009/06/12 · openalex publication_date 2010/02/05 · arxiv updated 2015/05/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
A scheme for generating a fractal butterfly Floquet spectrum, first proposed by Wang and Gong [Phys. Rev. A 77, 031405(R) (2008)], is extended to driven SU(2) systems such as a driven two-mode Bose-Einstein condensate. A class of driven systems without a link with the Harper-model context is shown to have an intriguing butterfly Floquet spectrum. The found butterfly spectrum shows remarkable deviations from the known Hofstadter's butterfly. In addition, the level crossings between Floquet states of the same parity and between Floquet states of different parities are studied and highlighted. The results are relevant to studies of fractal statistics, quantum chaos, and coherent destruction of tunneling, as well as the validity of mean-field descriptions of Bose-Einstein condensates.