Ergodicity of a Singly-thermostated Harmonic Oscillator

William Graham Hoover^a, Julien Clinton Sprott^b, Carol Griswold Hoover^a
^aRuby Valley Research Instiutute, Highway Contract 60, Box 601, Ruby Valley, NV 89833, USA
^bDepartment of Physics,, University of Wisconsin--Madison, WI 53706, USA

Received 25 June 2015, Revised 22 August 2015, Accepted 25 August 2015, Available online 1 September 2015

ABSTRACT

Although Nosé's thermostated mechanics is formally consistent with Gibbs' canonical ensemble, the thermostated Nosé-Hoover (harmonic) oscillator, with its mean kinetic temperature controlled, is far from ergodic, Much of its phase space is occupied by regular conservative tori. Oscillator ergodicity has previously been achieved by controlling two oscillator moments with two thermostat variables. Here we use computerized searches in conjunction with visualization to find singly-thermostated motion equations for the oscillator which are consistent with Gibbs' canonical distribution. Such models are the simplest able to bridge the gap between Gibbs' statistical ensembles and Newtonian single-particle dynamics.

Ref: W. G. Hoover, J. C. Sprott, and C. G. Hoover, Commun. Nonlinear Sci. Numer. Simulat. 32, 234-240 (2016)

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