Quantum signatures of an integrable system with a chaotic scattering map

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Abstract
A rather simple completely integrable Hamiltonian with a chaotic classical scattering map is analysed in quantum mechanics. After the analytical computation of the S-matrix we investigate numerically the distribution of scattering phases, giving the nearest-neighbour distribution, the number variance and the Fourier transform of the spectrum. We find fair agreement with the random matrix prediction for the circular orthogonal ensemble (COE) as appropriate for the time-reversal invariant system with a chaotic scattering map. This example confirms that COE properties of the S-matrix do not necessarily indicate topological chaos in the flow generated by the classical Hamiltonian.