Pathways of activated escape in periodically modulated systems

TL;DR

This paper studies how systems escape from states under periodic modulation, revealing the shape and distribution of escape trajectories, with analytical and simulation results showing multiple peaks in the escape distribution.

Contribution

It introduces a detailed analysis of escape trajectories forming diffusion tubes in periodically modulated systems, including their shape and distribution, supported by analytical and simulation evidence.

Findings

Escape trajectories form diffusion tubes that repeat periodically.

The distribution of escape points can have multiple peaks separated by the modulation period.

Analytical results align with Brownian particle simulations in modulated potentials.

Abstract

We investigate dynamics of activated escape in periodically modulated systems. The trajectories followed in escape form diffusion broadened tubes, which are periodically repeated in time. We show that these tubes can be directly observed and find their shape. Quantitatively, the tubes are characterized by the distribution of trajectories that, after escape, pass through a given point in phase space for a given modulation phase. This distribution may display several peaks separated by the modulation period. Analytical results agree with the results of simulations of a model Brownian particle in a modulated potential.