Analytic dynamics of one-dimensional particle system with strong interaction

TL;DR

This paper analyzes the early-time behavior of a system of electrons on a circle with Coulomb repulsion, providing estimates on the convergence of velocity series and implications for rapid electric current establishment.

Contribution

It offers new estimates on the convergence radius of velocity series in a strongly interacting particle system, linking dynamics to electric current formation.

Findings

Derived lower bounds for convergence radius of velocity series

Connected particle dynamics to electric current development

Provided mathematical estimates relevant for fast current establishment

Abstract

We study here the small time dynamics of $N$ electrons on the circle with Coul;omb repulsive interaction and study the series for the velocities (initially zero). The main result is the estimates of the convergence radius from below. We explain how this result is related to the problem of very fast establishing of direct electric current.