论文标题
简单谐波振荡器合奏的稳定性分析
Stability analysis of an ensemble of simple harmonic oscillators
论文作者
论文摘要
在本文中，我们研究了与位移平方成正比的谐波振荡器电位构型的稳定性。由于参数的变化，我们在分区函数中得出波动的表达式。质量，温度和振荡器的频率。在这里，我们将分区函数的Hessian矩阵介绍为从参数空间到实数集的模型嵌入函数。在此框架中，我们将谐波振荡器波动的参数空间中的区域分类，它们产生稳定的统计配置。稳定性的机制遵循波动理论的概念。在第7和第8节中，我们提供了系统和稳定区域的本质，在该区域中，该系统得出稳定或不稳定的统计基础，或者它经历了几何相变。最后，在$ 9 $中，对结果进行了比较，参考了其他现有研究。
In this paper, we investigate the stability of the configurations of harmonic oscillator potential that are directly proportional to the square of the displacement. We derive expressions for fluctuations in partition function due to variations of the parameters, viz. the mass, temperature and the frequency of oscillators. Here, we introduce the Hessian matrix of the partition function as the model embedding function from the space of parameters to the set of real numbers. In this framework, we classify the regions in the parameter space of the harmonic oscillator fluctuations where they yield a stable statistical configuration. The mechanism of stability follows from the notion of the fluctuation theory. In sections 7 and 8, we provide the nature of local and global correlations and stability regions where the system yields a stable or unstable statistical basis, or it undergoes into geometric phase transitions. Finally, in section $9$, the comparison of results is provided with reference to other existing research.
