Record statistics in random vectors and quantum chaos

TL;DR

This paper analytically studies record statistics in complex random states and quantum chaos, revealing how correlations affect record distributions and their growth with system size.

Contribution

It provides an analytical calculation of record statistics in random states and explores the impact of correlations in quantum chaos using the standard map.

Findings

Record intensity probability follows a Bernoulli process.

Correlation due to normalization alters the record distribution from universal forms.

Number of intensity records scales as a power law in mixed phase space regimes.

Abstract

The record statistics of complex random states are analytically calculated, and shown that the probability of a record intensity is a Bernoulli process. The correlation due to normalization leads to a probability distribution of the records that is non-universal but tends to the Gumbel distribution asymptotically. The quantum standard map is used to study these statistics for the effect of correlations apart from normalization. It is seen 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 random states.