Canonical dynamics of the Nosé oscillator: Stability, order, and chaos

Harald A. Posch, William G. Hoover, and Franz J. Vesely
Phys. Rev. A 33, 4253 – Published 1 June 1986
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Abstract

Nosé has developed many-body equations of motion designed to reproduce Gibbs’s canonical phase-space distribution. These equations of motion have a Hamiltonian basis and are accordingly time reversible and deterministic. They include thermodynamic temperature control through a single deterministic friction coefficient, which can be thought of as a control variable or as a memory function. We apply Nosé’s ideas to a single classical one-dimensional harmonic oscillator. This relatively simple system exhibits both regular and chaotic dynamical trajectories, depending on the initial conditions. We explore here the nature of these solutions by estimating their fractal dimensionality and Lyapunov instability. The Nosé oscillator is a borderline case, not sufficiently chaotic for a fully statistical description. We suggest that the behavior of only slightly more complicated systems is considerably simpler and in accord with statistical mechanics.

  • Received 11 November 1985

DOI:https://doi.org/10.1103/PhysRevA.33.4253

©1986 American Physical Society

Authors & Affiliations

Harald A. Posch, William G. Hoover, and Franz J. Vesely

  • Institut für Experimentalphysik, Universitat Wien, Boltzmanngasse 5, A-1090 Vienna, Austria

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Issue

Vol. 33, Iss. 6 — June 1986

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