$1/f^{\alpha}$ noise in the Robin Hood model

TL;DR

This paper investigates the presence of 1/f^α noise in the Robin Hood model, revealing nontrivial spectral exponents and analyzing temporal correlations in force fluctuations and extremal site dynamics.

Contribution

It provides the first detailed analysis of the power spectra and critical exponents in the Robin Hood model, highlighting the emergence of 1/f^α noise in this self-organized critical system.

Findings

Identification of 1/f^α noise with 0<α<2 in local force fluctuations.

Scaling functions and critical exponents derived from finite-size scaling.

Analysis of temporal fluctuations in extremal site position and activity signals.

Abstract

We consider the Robin Hood dynamics, a one-dimensional extremal self-organized critical model that describes the evolution of low-temperature creep. One of the key quantities is the time evolution of the state variable (force noise). To understand the temporal correlations, we compute the power spectra of the local force fluctuations and apply finite-size scaling to get scaling functions and critical exponents. We find a signature of the $1/f^{\alpha}$ noise for the local force with a nontrivial value of the spectral exponent $0< \alpha < 2$. We also examine temporal fluctuations in the position of the extremal site and a local activity signal. We present results for different local interaction rules of the model.