Using the Hadamard and related transforms for simplifying the spectrum of the quantum baker's map

Abstract

We rationalize the somewhat surprising efficacy of the Hadamard transform in simplifying the eigenstates of the quantum baker's map, a paradigmatic model of quantum chaos. This allows us to construct closely related, but new, transforms that do significantly better, thus nearly solving for many states of the quantum baker's map. These new transforms, which combine the standard Fourier and Hadamard transforms in an interesting manner, are constructed from eigenvectors of the shift permutation operator that are also simultaneous eigenvectors of bit-flip (parity) and possess bit-reversal (time-reversal) symmetry.

arXiv commentVersion to appear in J. Phys. A. Added discussions; modified title; corrected minor errors

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Cited by in corpus (4)

• Generating a Fractal Butterfly Floquet Spectrum in a Class of Driven SU(2) Systems: Eigenstate Statistics
• Quantum chaos in the spectrum of operators used in Shor's algorithm
• Generalized Quantum Baker Maps as perturbations of a simple kernel
• The modular multiplication operator and the quantized bakers maps