Ergodicity of a Singly-thermostated Harmonic Oscillator
William Graham Hoovera, Julien
Clinton Sprottb, Carol Griswold Hoovera
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
Although Nosť's thermostated mechanics is formally consistent with
Gibbs' canonical ensemble, the thermostated Nosť-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
Ref: W. G. Hoover, J. C. Sprott, and C. G. Hoover, Commun.
Nonlinear Sci. Numer. Simulat. 32, 234-240 (2016)
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