Ergodic Isoenergetic Molecular Dynamics for Microcanonical-Ensemble Averages

TL;DR

This paper introduces a novel ergodic isoenergetic molecular dynamics method that uses random velocity rotations to achieve full phase space coverage for microcanonical ensemble averages, avoiding typical chaotic behavior.

Contribution

It presents a time-reversible, energy-conserving approach to ergodic microcanonical dynamics by adding random velocity rotations, extending ergodic techniques beyond isothermal systems.

Findings

Successfully achieves ergodic coverage of the energy shell.

Avoids Poincaré-section holes and island chains.

Demonstrated on a 2D cell model with scatterers.

Abstract

Considerable research has led to ergodic isothermal dynamics which can replicate Gibbs' canonical distribution for simple ( small ) dynamical problems. Adding one or two thermostat forces to the Hamiltonian motion equations can give an ergodic isothermal dynamics to a harmonic oscillator, to a quartic oscillator, and even to the "Mexican-Hat" ( double-well ) potential problem. We consider here a time-reversible dynamical approach to Gibbs' "microcanonical" ( isoenergetic ) distribution for simple systems. To enable isoenergetic ergodicity we add occasional random rotations to the velocities. This idea conserves energy exactly and can be made to cover the entire energy shell with an ergodic dynamics. We entirely avoid the Poincar\'e-section holes and island chains typical of Hamiltonian chaos. We illustrate this idea for the simplest possible two-dimensional example, a single particle moving in a periodic square-lattice array of scatterers, the "cell model".