Hyperradial distribution function of few-body problems: a new arena for extreme value theory

TL;DR

This paper investigates the hyperradial distribution in few-body systems with van der Waals and charged-induced dipole interactions, revealing a universal Fréchet distribution pattern linked to extreme value theory.

Contribution

It introduces a novel connection between extreme value theory and few-body physics by showing the universal hyperradial distribution follows a Fréchet distribution.

Findings

Hyperradial distribution follows a Fréchet distribution.

Universal behavior independent of particle number and interaction type.

Establishes a link between extreme value theory and few-body physics.

Abstract

This work explores classical capture models for few-body systems via a Monte Carlo method in hyperspherical coordinates. In particular, we focus on van der Waals and charged-induced dipole interactions. As a result, we notice that, independently of the number of particles and interparticle interaction, the capture hyperradial distribution function follows a Fr\'echet distribution, a special type of the generalized extreme value distribution. Besides, we elaborate on the fundamentals of such universal feature using the general extreme value theory, thus, establishing a connection between extreme value theory and few-body physics.