Record statistics in random vectors and quantum chaos

The record statistics of the quantum standard map is shown to capture the classical transition to chaos. It is shown that in the mixed phase-space regime the number of intensity records is a power law in the dimensionality of the state as opposed to the logarithmic growth for the random states. The exponent of this power law is close to 0.5 at the critical value of the chaos parameter, K ≃ 0.98 of the standard map, an exponent that is also obtained for random walks. These findings are based on the record statistics of complex, normalized random states for which we have shown that the probability of a record intensity is a Bernoulli process. © EPLA, 2013.