A simple proof and a detailed analysis of the nonergodicity for
multidimensional harmonic oscillator systems with the Nosé – Hoover-type
thermostat are presented. The origin of the nonergodicity is the symmetries in
the multidimensional target physical system, and it differs from that in the
Nosé – Hoover thermostat with the one-dimensional harmonic oscillator. A
new and simple deterministic method to recover the ergodicity is also
proposed. An individual thermostat variable is attached to each degree of
freedom, and all of these variables act on a friction coefficient for each
degree of freedom. This action is linear and controlled by a Nosé mass
matrix $\mathbf{Q}$, which is the matrix analogue of the scalar Nosé mass.
The matrix $\mathbf{Q}$ can break the symmetry and contribute to the ergodicity.
Keywords:
ergodicity, Nosé – Hoover equation, thermostat, molecular dynamics, invariant space, multidimensional harmonic oscillator, Nosé-mass matrix, density dynamics
Citation:
Fukuda I., Moritsugu K., Fukunishi Y., On Ergodicity for Multidimensional Harmonic Oscillator Systems with Nosé – Hoover-type Thermostat, Regular and Chaotic Dynamics,
2021, Volume 26, Number 2,
pp. 183-204