Measure for chaotic scattering amplitudes

TL;DR

This paper introduces a new measure for chaotic scattering amplitudes based on a log-normal distribution of ratios of peak spacings, applicable across quantum scattering and string decay, and linked to Riemann zeta zeros.

Contribution

It proposes a universal measure for chaotic scattering amplitudes that applies to quantum systems, string decay, and relates to the zeros of the Riemann zeta function.

Findings

The measure follows a log-normal distribution for the ratios of peak spacings.

It applies to quantum scattering on a leaky torus.

It matches the distribution governing the zeros of the Riemann zeta function.

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.