Measure for chaotic scattering amplitudes

Abstract

We propose a novel measure of chaotic scattering amplitudes. It takes the form of a log-normal distribution function for the ratios $r_n={\delta_n}/{\delta_{n+1}}$ of (consecutive) spacings $\delta_n$ between two (consecutive) peaks of the scattering amplitude. We show that the same measure applies to the quantum mechanical scattering on a leaky torus as well as to the decay of highly excited string states into two tachyons. Quite remarkably the $r_n$ obey the same distribution that governs the non-trivial zeros of Riemann zeta function.