具有Nose-Hoover型恒温器的多维谐振子系统的遍历性
On ergodicity for multi-dimensional harmonic oscillator systems with Nose-Hoover type thermostat
摘要：
对具有Nose-Hoover型恒温器的多维谐振子系统的非遍历性给出了简单的证明和详细的分析。非遍历性的起源是多维目标物理系统的对称性，不同于一维谐振子Nose-Hoover恒温器的非遍历性。还提出了一种新的恢复遍历性的简单确定性方法。每个自由度都有一个独立的恒温器变量，所有这些变量都作用于每个自由度的摩擦系数。这个作用是线性的，并且由Nosé质量矩阵Q控制，它是标量Nosé质量的矩阵模拟。矩阵Q可以打破对称性，并有助于达到遍历性。
英文摘要：
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.
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