Chirikov criterion of resonance overlapping for the model of molecular dynamics

TL;DR

This paper applies the Chirikov resonance overlap criterion to a molecular dynamics model with Lennard-Jones interactions, deriving asymptotic expressions at different energy levels to predict chaotic behavior.

Contribution

It introduces an asymptotic representation of the Chirikov criterion specific to a Lennard-Jones particle chain model, enhancing understanding of chaos onset in molecular systems.

Findings

Asymptotic formulas for the resonance overlap function at low energies

Asymptotic formulas for the resonance overlap function at high energies

Validation of the Chirikov criterion as a chaos predictor in molecular dynamics

Abstract

The chaotic dynamics in a cell of particles' chain interacting by means of Lennard-Jones potential is considered. Chirikov criterion of resonance over- lapping is used as the condition of chaos. The asymptotic representation for this function at low and high energies is obtained for the function corresponding to the criterion.