Ikuo Fukuda

Kobe 650-0047
University of Hyogo


Fukuda I., Moritsugu K., Fukunishi Y.
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, vol. 26, no. 2, pp. 183-204

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