2006/03/31 by Arul Lakshminarayan, N. Meenakshisundaram · 1 citation
Computer Science · Physics and Astronomy · #Chaos control and synchronization #Neural Networks and Reservoir Computing #Quantum chaos and dynamical systems #cond-mat.other #nlin.CD #quant-ph
paper · pdf · doi:10.1088/0305-4470/39/36/006
published as J. Phys. A: Math. Gen. 39 (2006) 11205-11216. · Version to appear in J. Phys. A. Added discussions; modified title; corrected minor errors
arxiv created 2006/08/14 · openalex publication_date 2006/08/18 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30
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 many states of the quantum baker's map. These 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.