The Fourier transform of the Hadamard transform: Multifractals, Sequences and Quantum Chaos

Details The Fourier transform of the Hadamard transform: Multifractals, Sequences and Quantum Chaos The Fourier transform of the Hadamard transform: Multifractals, Sequences and Quantum Chaos

2005-10-05

arxiv.org/abs/nlin/0510009v2

Proceedings of the National Conference on Nonlinear Systems and Dynamics, edited by M. Lakshmanan and R. Sahadevan (Allied Pub

Nonlinear Sciences

Chaotic Dynamics

4 pages

Scientific paper

We introduce a class of functions that limit to multifractal measures and which arise when one takes the Fourier transform of the Hadamard transform. This introduces generalizations of the Fourier transform of the well-studied and ubiquitous Thue-Morse sequence, and introduces also generalizations to other intriguing sequences. We show their relevance to quantum chaos, by displaying quantum eigenfunctions of the quantum bakers map that are approximated well by such measures, thereby extending our recent work where we pointed to the existence of ``Thue-Morse'' states.

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