Stochastic versus dynamic approach to Levy statistics in the presence of an external perturbation

TL;DR

This paper investigates how dissipation affects diffusion processes driven by slow fluctuations, revealing conditions under which systems exhibit Gaussian or Levy statistics depending on fluctuation correlation properties.

Contribution

It introduces a numerical analysis of the transition boundary between Gaussian and Levy regimes in dissipative diffusion systems influenced by external perturbations.

Findings

System exhibits Gaussian or Levy statistics depending on fluctuation correlation.

Transition boundary between statistical regimes identified numerically.

Dissipation influences the dominant diffusion behavior.

Abstract

We study the influence of a dissipation process on diffusion dynamics triggered by slow fluctuations. We study both strong- and weak-friction regime. When the latter regime applies, the system is attracted by the basin of either Gauss or Levy statistics according to whether the fluctuation correlation function is integrable or not. We analyze with a numerical calculation the border between the two basins of attraction.