Diffusion in Fluctuating Media: The Resonant Activation Problem

TL;DR

This paper investigates diffusion in a fluctuating one-dimensional lattice with combined deterministic and stochastic state transitions, revealing a double resonant activation phenomenon affecting key diffusion metrics.

Contribution

It introduces a novel model of diffusion in a multi-state fluctuating medium and analyzes resonant activation effects on diffusion properties.

Findings

Double resonant activation observed in MFPT and return probability.

Resonant phenomena depend on the stochastic transition rate intensity.

Model provides insights into diffusion in complex fluctuating environments.

Abstract

We present a one-dimensional model for diffusion in a fluctuating lattice; that is a lattice which can be in two or more states. Transitions between the lattice states are induced by a combination of two processes: one periodic deterministic and the other stochastic. We study the dynamics of a system of particles moving in that medium, and characterize the problem from different points of view: mean first passage time (MFPT), probability of return to a given site ($P_{s_0}$), and the total length displacement or number of visited lattice sites ($\Lambda$). We observe a double {\it resonant activation}-like phenomenon when we plot the MFPT and $P_{s_0}$ as functions of the intensity of the transition rate stochastic component.