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Volume 24 (2) 2018, 155–158

Ergodic Isoenergetic Molecular Dynamics for Microcanonical-Ensemble Averages

Hoover Wm.G. , Hoover C.G.

Ruby Valley Research Institute
Highway Contract 60, Box 601, Ruby Valley, Nevada 89833, USA
E-mail: hooverwilliam@yahoo.com

Received:

Received: 25 June 2018; revised: 26 June 2018; accepted: 26 June 2018; published online: 30 June 2018

DOI:   10.12921/cmst.2018.0000035

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” (doublewell) 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 Poincaré-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”.

Key words:

algorithms, chaos, ergodicity, Lyapunov exponent

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