On ergodicity for multi-dimensional harmonic oscillator systems with Nose-Hoover type thermostat
Abstract
A simple proof and detailed analysis on the non-ergodicity for multidimensional harmonic oscillator systems with Nose-Hoover type thermostat are given. The origin of the nonergodicity is symmetries in the multidimensional target physical system, and is differ from that in the Nose-Hoover thermostat with the 1-dimensional harmonic oscillator. A new simple deterministic method to recover the ergodicity is also presented. An individual thermostat variable is attached to each degree of freedom, and all these variables act on a friction coefficient for each degree of freedom. This action is linear and controlled by a Nos\'e mass matrix Q, which is a matrix analogue of the scalar Nos\'e's mass. Matrix Q can break the symmetry and contribute to attain the ergodicity.
Keywords
Cite
@article{arxiv.2008.07917,
title = {On ergodicity for multi-dimensional harmonic oscillator systems with Nose-Hoover type thermostat},
author = {Ikuo Fukuda and Kei Moritsugu and Yoshifumi Fukunishi},
journal= {arXiv preprint arXiv:2008.07917},
year = {2021}
}