Spectral statistics of a quantum interval-exchange map

Details Spectral statistics of a quantum interval-exchange map Spectral statistics of a quantum interval-exchange map

2004-08-31

arxiv.org/abs/nlin/0408062v1

Nonlinear Sciences

Chaotic Dynamics

4 pages, 3 figures

Scientific paper

10.1103/PhysRevLett.93.254102

Curious spectral properties of an ensemble of random unitary matrices appearing in the quantization of a map p -> p+alpha, q -> q+f(p+alpha) in [Giraud et al. nlin.CD/0403033] are investigated. When alpha=m/n with integer co-prime m,n and matrix dimension N -> infinity is such that mN = 1 or -1 mod n, local spectral statistics of this ensemble tends to the semi-Poisson distribution [Bogomolny et al. Eur. Phys. J. B 19, 121 (2001)] with arbitrary integer or half-integer level repulsion at small distances: R(s)-> s^{beta} when s -> 0 and beta=n-1 or n/2-1 depending on time-reversal symmetry of the map.

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