Anomalous escape governed by thermal 1/f noise

TL;DR

This paper analytically investigates how thermal 1/f noise influences the subdiffusive escape of particles from a potential well, revealing a power-law escape behavior that varies with barrier height and temperature.

Contribution

It introduces a generalized Langevin approach to analytically describe anomalous escape driven by thermal 1/f noise, contrasting with traditional fractional Fokker-Planck models.

Findings

Escape follows a power-law asymptotically with an exponent depending exponentially on barrier height and temperature.

The results provide a way to experimentally distinguish between different subdiffusive escape mechanisms.

The study offers a mathematical framework for understanding noise-driven anomalous escape processes.

Abstract

We present an analytic study for subdiffusive escape of overdamped particles out of a cusp-shaped parabolic potential well which are driven by thermal, fractional Gaussian noise with a $1/\omega^{1-\alpha}$ power spectrum. This long-standing challenge becomes mathematically tractable by use of a generalized Langevin dynamics via its corresponding non-Markovian, time-convolutionless master equation: We find that the escape is governed asymptotically by a power law whose exponent depends exponentially on the ratio of barrier height and temperature. This result is in distinct contrast to a description with a corresponding subdiffusive fractional Fokker-Planck approach; thus providing experimentalists an amenable testbed to differentiate between the two escape scenarios.