On Ergodicity for Multi-Dimensional Harmonic Oscillator Systems with Nose--Hoover Type Thermostat
On Ergodicity for Multi-Dimensional Harmonic Oscillator Systems with Nose--Hoover Type Thermostat
复制标题
鼻式多维谐波振荡器系统的遍历性--胡佛式恒温器
DOI：
10.1134/s1560354721020064
复制
发表时间：
2021
影响因子：
1.4
通讯作者：
and Yoshifumi Fukunishi
中科院分区：
文献类型：
--
作者：
Ikuo Fukuda;Kei Moritsugu;and Yoshifumi Fukunishi
给出了具有Nosé-Hoover型恒温器的多维谐振子系统的非遍历性的简单证明和详细分析。这种非遍历性的起源是多维目标物理系统的对称性，它不同于一维谐振子的Nosé-Hoover恒温器的非遍历性。提出了一种新的、简单的确定恢复遍历性的方法。每个自由度都附加了一个单独的恒温器变量，所有这些变量都作用于每个自由度的摩擦系数。这一作用是线性的，并由诺塞质量矩阵控制，诺塞质量矩阵是标量诺塞质量的矩阵模拟。矩阵会破坏对称性，导致遍历。
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, which is the matrix analogue of the scalar Nosé mass. The matrixcan break the symmetry and contribute to the ergodicity.