Hamiltonian dynamics of homopolymer chain models

TL;DR

This paper investigates the Hamiltonian dynamics of homopolymer chain models, revealing a transition between slow and fast phase space mixing and detecting the theta-transition through Lyapunov exponents, providing insights beyond traditional statistical mechanics.

Contribution

It introduces a dynamical approach to homopolymer models, uncovering a nontrivial phase space transition and identifying the theta-transition via Lyapunov exponents, which are not accessible through standard statistical methods.

Findings

Reproduction of statistical mechanics results through dynamical time averages.

Identification of a transition between slow and fast phase space mixing regimes.

Detection of the theta-transition via changes in the Lyapunov exponent.

Abstract

The Hamiltonian dynamics of chains of nonlinearly coupled particles is numerically investigated in two and three dimensions. Simple, off-lattice homopolymer models are used to represent the interparticle potentials. Time averages of observables numerically computed along dynamical trajectories are found to reproduce results given by the statistical mechanics of homopolymer models. The dynamical treatment, however, indicates a nontrivial transition between regimes of slow and fast phase space mixing. Such a transition is inaccessible to a statistical mechanical treatment and reflects a bimodality in the relaxation of time averages to corresponding ensemble averages. It is also found that a change in the energy dependence of the largest Lyapunov exponent indicates the theta-transition between filamentary and globular polymer configurations, clearly detecting the transition even for a finite number of particles.