Abstract
We investigate quantized maps of the torus whose classical analogues are ergodic but not mixing. Their quantum spectral statistics shows non-generic behaviour, i.e. it does not follow random matrix theory (RMT). By coupling the map to a spin 1/2, which corresponds to changing the quantization without altering the classical limit of the dynamics on the torus, we numerically observe a transition to RMT statistics. The results are interpreted in terms of semiclassical trace formulae for the maps with and without spin, respectively. We thus have constructed quantum systems with non-mixing classical limit which show generic (i.e. RMT) spectral statistics. We also discuss the analogous situation for an almost-integrable map, where we compare to semi-Poissonian statistics.
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