论文标题
关于具有鼻型恒温器的多维谐波振荡器系统的Ergodicity
On ergodicity for multi-dimensional harmonic oscillator systems with Nose-Hoover type thermostat
论文作者
论文摘要
对具有鼻型式恒温器的多维谐波振荡系统的非效应性的简单证明和详细分析。非连接性的起源是多维目标物理系统中的对称性，并且与使用1维谐波振荡器的鼻子恒温器中的对称性不同。还提出了一种新的简单确定性方法，以恢复过时性。单个恒温器变量附着在每个自由度上，所有这些变量都针对每个自由度的摩擦系数作用。该动作是线性的，并由Nosé质量矩阵Q控制，这是标量Nosé质量的基质类似物。矩阵Q可以打破对称性并有助于达到终身性。
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 Nosé mass matrix Q, which is a matrix analogue of the scalar Nosé's mass. Matrix Q can break the symmetry and contribute to attain the ergodicity.
