Universality of residence-time distributions in non-adiabatic stochastic resonance

TL;DR

This paper derives universal, mathematically rigorous expressions for residence-time and first-passage-time distributions of a periodically forced Brownian particle in a bistable potential, revealing their near-universal exponential form modulated periodically.

Contribution

It introduces universal functions governing the distributions' periodic modulations, valid across a wide range of forcing frequencies and amplitudes.

Findings

Distributions are close to periodically modulated exponential forms.

Universal functions depend on a single parameter related to forcing period.

Analysis includes behavior in low- and high-frequency limits.

Abstract

We present mathematically rigorous expressions for the residence-time and first-passage-time distributions of a periodically forced Brownian particle in a bistable potential. For a broad range of forcing frequencies and amplitudes, the distributions are close to periodically modulated exponential ones. Remarkably, the periodic modulations are governed by universal functions, depending on a single parameter related to the forcing period. The behaviour of the distributions and their moments is analysed, in particular in the low- and high-frequency limits.