Extended-phase-space isothermal molecular dynamics: Canonical harmonic oscillator

A modified set of equations is given for the simulation of a canonical ensemble based on the method introduced by Nos\'e. The equations produce trajectories that are sufficiently chaotic to calculate average properties of a canonical ensemble, even for a small number of degrees of freedom. This important fact is demonstrated by presenting results for a single one-dimensional harmonic oscillator. It is shown that the extended system is chaotic and that the trajectories cover the whole energy surface in phase space.