Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On ergodicity for multi-dimensional harmonic oscillator systems with
  Nose-Hoover type thermostat   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.

27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
30
The categories of this paper are: q-alg
14
The categories of this paper are: math-ph
6
The categories of this paper are: astro-ph
2
The categories of this paper are: math
28
The categories of this paper are: alg-geom
22
The categories of this paper are: chao-dyn
13
The categories of this paper are: quant-ph
36
The categories of this paper are: cmp-lg
33
The categories of this paper are: plasm-ph
31
The categories of this paper are: ao-sci
25
The categories of this paper are: patt-sol
7
The categories of this paper are: hep-th
1
The categories of this paper are: cs
26
The categories of this paper are: bayes-an