Modified Nosé-Hoover equation for a one-dimensional oscillator: Enforcement of the virial theorem

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Abstract
Recently, attempts have been made to alter the equation of motion of a multiparticle system so that the temperature rather than the energy is constant. The Nosé-Hoover equation of motion is very useful for systems with a large number of particles, but, for a one-dimensional oscillator, the phase-space dynamics is not sufficiently chaotic for a fully statistical description. We propose a modified Nosé-Hoover equation, obtained by enforcing the virial theorem, for which the phase-space dynamics is much more chaotic. This modified Nosé-Hoover equation is easily generalized and may be useful for other systems with a small number of particles.