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.

v2: small corrections, references added; v3: minor improvements to match published version

References in corpus (10)

• Localization of interacting fermions at high temperature
• Signatures of Chaos in Non-integrable Models of Quantum Field Theory
• Higher Spin Scattering in Superstring Theory
• Chaos in a many-string scattering amplitude
• Bounds on quantum evolution complexity via lattice cryptography
• Covariant Closed String Coherent States
• On stable higher spin states in Heterotic String Theories
• Photon emission from an excited string
• Transient chaos analysis of string scattering
• Chaotic instability in the BFSS matrix model

Cited by in corpus (7)

• The chaotic emergence of thermalization in highly excited string decays
• Weak chaos and mixed dynamics in the string S-matrix
• Chaotic and Thermal Aspects in the Highly Excited String S-Matrix
• Correlation functions for open strings and chaos
• String amplitudes and mutual information in confining backgrounds: the partonic behavior
• From Confinement to Chaos in AdS/CFT Correspondence via Non-equilibrium Local States
• Classical string profile for a class of DDF amplitudes