Please use this identifier to cite or link to this item: https://doi.org/10.1103/PhysRevE.81.066212
Title: Generating a fractal butterfly Floquet spectrum in a class of driven SU(2) systems: Eigenstate statistics
Authors: Bandyopadhyay, J.N. 
Wang, J.
Gong, J. 
Issue Date: 18-Jun-2010
Source: Bandyopadhyay, J.N., Wang, J., Gong, J. (2010-06-18). Generating a fractal butterfly Floquet spectrum in a class of driven SU(2) systems: Eigenstate statistics. Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 81 (6) : -. ScholarBank@NUS Repository. https://doi.org/10.1103/PhysRevE.81.066212
Abstract: The Floquet spectra of a class of driven SU(2) systems have been shown to display butterfly patterns with multifractal properties. The implication of such critical spectral behavior for the Floquet eigenstate statistics is studied in this work. Following the methodologies for understanding the fractal behavior of energy eigenstates of time-independent systems on the Anderson transition point, we analyze the distribution profile, the mean value, and the variance of the logarithm of the inverse participation ratio of the Floquet eigenstates associated with multifractal Floquet spectra. The results show that the Floquet eigenstates also display fractal behavior but with features markedly different from those in time-independent Anderson-transition models. This motivated us to propose random unitary matrix ensemble, called "power-law random banded unitary matrix" ensemble, to illuminate the Floquet eigenstate statistics of critical driven systems. The results based on the proposed random matrix model are consistent with those obtained from our dynamical examples with or without time-reversal symmetry. © 2010 The American Physical Society.
Source Title: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
URI: http://scholarbank.nus.edu.sg/handle/10635/52954
ISSN: 15393755
DOI: 10.1103/PhysRevE.81.066212
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