Nonintegrability and fluctuation by symmetry violation in perturbed harmonic oscillator systems

Details Nonintegrability and fluctuation by symmetry violation in perturbed harmonic oscillator systems Nonintegrability and fluctuation by symmetry violation in perturbed harmonic oscillator systems

2007-02-13

arxiv.org/abs/cond-mat/0702297v1

Physics

Condensed Matter

Statistical Mechanics

13 pages, 40 figures

Scientific paper

The violation of symmetry between the time series of elongation and contraction rates of phase-space point spacings is studied to examine the chaos in perturbed harmonic oscillator systems. A transition from integrability to nonintegrability is quantitatively evaluated by introducing a correlation coefficient for the degree of symmetry violation. A feature of the correlation coefficient is discussed, suggesting a possible advantage over the Lyapunov exponent. The relationship between a fluctuation property based on symmetry violation and nonintegrability is also discussed.

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