A universal mechanism for long-range cross-correlations

¹ Department of Physics, University of Warwick - Coventry CV4 7AL, UK
² Department of Physics, University of Athens - GR-15771 Athens, Greece
³ Zentrum für Optische Quantentechnologien, Universität Hamburg - Luruper Chaussee 149, D-22761 Hamburg, Germany
⁴ The Hamburg Centre for Ultrafast Imaging - Luruper Chaussee 149, D-22761 Hamburg, Germany

Received: 16 September 2013
Accepted: 16 January 2014

Abstract

Cross-correlations are thought to emerge through interaction between particles. Here we present a universal dynamical mechanism capable of generating power-law cross-correlations between non-interacting particles exposed to an external potential. This phenomenon can occur as an ensemble property when the external potential induces intermittent dynamics of Pomeau-Manneville type, providing laminar and stochastic phases of motion in a system with a large number of particles. In this case, the ensemble of particle-trajectories forms a random fractal in time. The underlying statistical self-similarity is the origin of the observed power-law cross-correlations. Furthermore, we have strong indications that a sufficient condition for the emergence of these long-range cross-correlations is the divergence of the mean residence time in the laminar phase of the single particle motion (sporadic dynamics). We argue that the proposed mechanism may be relevant for the occurrence of collective behaviour in critical systems.