A cutoff time scaling of 1/f noise in a sandpile

Abstract

Abstract We show that for fluctuations in a sandpile with spectrum, the power may also exhibit a scaling with its cutoff time. Despite significant progress, this generic behaviour remains so far overlooked and poorly understood. An intriguing example is the power spectrum of a simple random walk (normal diffusive process) on a ring with L sites, showing behaviour instead of (Brownian noise) in the frequency regime . We address the intriguing problem by scaling method and discuss its relevance in the context of the sandpile system and a class of stochastic processes.