2007/11/13 by J. Martin, John Martin, Olivier Giraud +3
Computer Science · Physics and Astronomy · #Chaos-based Image/Signal Encryption #Quantum chaos and dynamical systems #Theoretical and Computational Physics #cond-mat.mes-hall #nlin.CD
paper · pdf · doi:10.1103/physreve.77.035201
published as Phys. Rev. E 77, 035201(R) (2008) · 4 pages, 4 figures
arxiv created 2007/11/13 · openalex publication_date 2008/03/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study multifractal properties of wave functions for a one-parameter family of quantum maps displaying the whole range of spectral statistics intermediate between integrable and chaotic statistics. We perform extensive numerical computations and provide analytical arguments showing that the generalized fractal dimensions are directly related to the parameter of the underlying classical map, and thus to other properties such as spectral statistics. Our results could be relevant for Anderson and quantum Hall transitions, where wave functions also show multifractality.