Multifractality and intermediate statistics in quantum maps

Details Multifractality and intermediate statistics in quantum maps Multifractality and intermediate statistics in quantum maps

2007-11-13

arxiv.org/abs/0711.2029v1

Phys. Rev. E 77, 035201(R) (2008)

Nonlinear Sciences

Chaotic Dynamics

4 pages, 4 figures

Scientific paper

10.1103/PhysRevE.77.035201

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.

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