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 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.

PACS numbers: 05.45.Mt, 02.30.Lt, 02.30.Nw, 03.67.Lx

Print publication: Issue 36 (8 September 2006)
Received 6 March 2006, in final form 6 July 2006
Published 18 August 2006