Stability analysis of an ensemble of simple harmonic oscillators

Author:

Thakur R. K.1,Tiwari B. N.2ORCID,Nigam R.13,Xu Y.4,Thiruvikraman P. K.1

Affiliation:

1. Department of Physics, Birla Institute of Technology & Science, Pilani Hyderabad Campus, Hyderabad 500078, India

2. INFN-Laboratori Nazionali di Frascati, Via Enrico Fermi 40, 00044 Frascati Rome, Italy

3. University of Information Science and Technology, “Saint Paul the Apostle”, Partizanska Str. bb, 6000 Ohrid, The Former Yugoslav Republic of Macedonia

4. Department of Applied Mathematics, School of Science, Northwestern Polytechnical University, Xi’an 710072, P. R. China

Abstract

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 Secs. 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 Sec. 9, the comparison of results is provided with reference to other existing research.

Publisher

World Scientific Pub Co Pte Lt

Subject

Condensed Matter Physics,Statistical and Nonlinear Physics

Reference47 articles.

1. N. Zettili, Quantum Mechanics: Concepts and Applications (Wiley-Blackwell, 2001), p. 93.

2. Reciprocal Relations in Irreversible Processes. I.

3. Fluctuations and Irreversible Processes

Cited by 1 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. On stability of thermodynamic systems: a fluctuation theory perspective;The European Physical Journal Plus;2023-06-13

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