Slow Relaxation and Phase Space Properties of a Conservative System with Many Degrees of Freedom

TL;DR

This study investigates how slow relaxation phenomena in a complex conservative system relate to phase space characteristics, revealing a dynamical crossover at a specific temperature across different regimes.

Contribution

It demonstrates a deep connection between relaxation slowdown and phase space properties in a one-dimensional discrete  model, using molecular dynamics simulations.

Findings

Identification of a dynamical crossover temperature

Correlation between Lyapunov spectrum and relaxation times

Consistency across different coupling regimes

Abstract

We study the one-dimensional discrete $\Phi^4$ model. We compare two equilibrium properties by use of molecular dynamics simulations: the Lyapunov spectrum and the time dependence of local correlation functions. Both properties imply the existence of a dynamical crossover of the system at the same temperature. This correlation holds for two rather different regimes of the system - the displacive and intermediate coupling regimes. Our results imply a deep connection between slowing down of relaxations and phase space properties of complex systems.