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}=δ_{n}/δ_{n+1} of (consecutive) spacings δ_{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 nontrivial zeros of Riemann ζ function.