1/f Noise and Long Configuration Memory in Bak-Tang-Wiesenfeld Models on Narrow Stripes

TL;DR

This paper demonstrates 1/f noise in narrow stripe Bak-Tang-Wiesenfeld sandpile models caused by exponentially long configuration memory, with analytical solutions revealing the broad distribution of time scales.

Contribution

It introduces an analytical approach to show how long configuration memory leads to 1/f noise in confined sandpile models.

Findings

1/f power spectrum observed in confined models

Long configuration memory causes broad time scale distribution

Analytical solutions confirm the mechanism for 1/f noise

Abstract

We report our findings of an 1/f power spectrum for the total amount of sand in directed and undirected Bak-Tang-Wiesenfeld models confined on narrow stripes and driven locally. The underlying mechanism for the 1/f noise in these systems is an exponentially long configuration memory giving rise to a very broad distribution of time scales. Both models are solved analytically with the help of an operator algebra to explicitly show the appearance of the long configuration memory.