Escape time, relaxation and sticky states of a softened Henon-Heiles model: low-frequency vibrational modes effects

TL;DR

This study investigates how weakening a low-frequency vibrational mode in a softened Henon-Heiles system accelerates relaxation, revealing exponential and power-law decay regimes, and identifying sticky states with quasiperiodic orbits.

Contribution

It introduces a simplified model to analyze the effects of mode softening on relaxation dynamics and sticky states in non-linear, non-equilibrium systems.

Findings

Weaker low-frequency modes lead to faster relaxation.

Relaxation exhibits exponential and power-law regimes depending on initial conditions.

Identification of sticky states with quasiperiodic orbits.

Abstract

Here we study the relaxation of a chain consisting of 3 masses joined by non-linear springs and periodic conditions when the stiffness is weakened. This system, when expressed in their normal coordinates, yields a softened Henon-Heiles system. By reducing the stiffness of one low-frequency vibrational mode, a faster relaxation is enabeled. This is due to a reduction of the energy barrier heights along the softened normal mode as well as for a widening of the opening channels of the energy landscape in configurational space. The relaxation is for the most part exponential, and can be explained by a simple flux equation. Yet, for some initial conditions the relaxation follows as a power law and, and in many cases, there is a regime change from exponential to power law decay. We pin point the initial conditions for the power law decay, finding two regions of sticky states. For such states, quasiperiodic orbits are found since almost for all components of the initial momentum orientation, the system is trapped inside two pockets of configurational space. The softened Henon- Heiles model presented here is intended as the simplest model in order to understand the interplay of rigidity, non-linear interactions and relaxation for non-equilibrium systems like glass-forming melts or soft-matter.