Abstract
The Nosé-Hoover dynamics is a deterministic method that is commonly used to sample the canonical Gibbs measure. This dynamics extends the physical Hamiltonian dynamics by the addition of a 'thermostat' variable, which is coupled nonlinearly with the physical variables. The accuracy of the method depends on the dynamics being ergodic. Numerical experiments have been published earlier that are consistent with non-ergodicity of the dynamics for some model problems. The authors recently proved the non-ergodicity of the Nosé-Hoover dynamics for the one-dimensional harmonic oscillator. In this paper, this result is extended to non-harmonic one-dimensional systems. We also show that, for some multidimensional systems, the averaged dynamics for the limit of infinite thermostat 'mass' has many invariants, thus giving theoretical support for either non-ergodicity or slow ergodization. Numerical experiments for a two-dimensional central force problem and the one-dimensional pendulum problem give evidence for non-ergodicity.
Original language | English (US) |
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Pages (from-to) | 1673-1694 |
Number of pages | 22 |
Journal | Nonlinearity |
Volume | 22 |
Issue number | 7 |
DOIs | |
State | Published - 2009 |