Topic area: CSCMP Spacing statistics of model spectra related to Farey sequences

One signature of quantum chaos is the failure of standard semiclassical (EBK) quantization due to the occurrence of chaotic ray paths in the WKB approximation. Another is the appearance of level repulsion in the statistics of the separation between nearest-neighbour eigenvalues, the primary diagnostic [2] being the probability distribution function (PDF), P(s), of the energy level separations, si ≡ Ei+1−Ei, with the energy scaled so as to make the average separation unity. Experimentally, the presence of quantum chaos might be seen as a lack of spatial coherence in wave activity.