title: Correlations of correlations: Secondary autocorrelations in finite harmonic systems.
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 show nonrandom long-time scale pattern, and higher-order correlations converge to the lowest normal mode.
authors.affiliation: Department of Computer Science, University of Toronto, Ontario M5S 2E4, Canada.
authors.forename: Dan
authors.initials: D
authors.lastname: Plyukhin
authors.affiliation: Department of Mathematics, Saint Anselm College, Manchester, New Hampshire 03102, USA.
authors.forename: Alex V
authors.initials: AV
authors.lastname: Plyukhin