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 shows non-random long-time scale pattern, and higher order correlations converge to the lowest normal mode.

9 pages, 6 figures

References in corpus (4)

• Fundamental Aspects of Quantum Brownian Motion
• Equilibration and Thermalization of Classical Systems
• Classical small systems coupled to finite baths
• Responses to applied forces and the Jarzynski equality in classical oscillator systems coupled to finite baths: An exactly solvable non-dissipative non-ergodic model