Stability analysis of an ensemble of simple harmonic oscillators

• Main Authors: Thakur, R. K, Tiwari, B. N, Nigam, R, Xu, Y, Thiruvikraman, P. K
• Format: Journal Article
• Language: English
• Published: 09-04-2020
• Subjects: Physics - Statistical Mechanics
• DOI: 10.48550/arxiv.2004.04737

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.