  Although Nose's thermostated mechanics is formally consistent with Gibbs'
canonical ensemble, the thermostated Nose-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. These models are the
simplest able to bridge the gap between Gibbs' statistical ensembles and
Newtonian single-particle dynamics.
