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arXiv · 1509.04359

Correlations of correlations: Secondary autocorrelations in finite harmonic systems

Dan Plyukhin·Alex V. Plyukhin
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Abstract

The momentum or velocity autocorrelation function C(t) for a tagged oscillator in a finite harmonic system decays like that of an infinite system for short times, but exhibits erratic behavior at longer time scales. We introduce the autocorrelation function of the long-time noisy tail of C(t) ("a correlation of the correlation"), which characterizes the distribution of recurrence times. Remarkably, for harmonic systems with same-mass particles this secondary correlation may coincide with the primary correlation C(t) (when both functions are normalized) either exactly, or over a significant initial time interval. When the tagged particle is heavier than the rest, the equality does not hold, correlations shows non-random long-time scale pattern, and higher order correlations converge to the lowest normal mode.

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Dan Plyukhin, Alex V. Plyukhin. 2015-12-21. Correlations of correlations: Secondary autocorrelations in finite harmonic systems. https://doi.org/10.1103/physreve.92.042101

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