Arrival time distribution for a driven system containing quenched dichotomous disorder

TL;DR

This paper investigates the distribution of arrival times for overdamped particles in a driven system with quenched dichotomous disorder, using path integral methods to analyze its properties and deviations from Gaussian behavior.

Contribution

It provides an explicit calculation of the arrival time distribution for a specific disorder case and analyzes its statistical properties and scaling behaviors.

Findings

Derived the characteristic function of the arrival time distribution.

Analyzed the distribution's behavior at different distances.

Quantified deviations from Gaussian shape via skewness and kurtosis.

Abstract

We study the arrival time distribution of overdamped particles driven by a constant force in a piecewise linear random potential which generates the dichotomous random force. Our approach is based on the path integral representation of the probability density of the arrival time. We explicitly calculate the path integral for a special case of dichotomous disorder and use the corresponding characteristic function to derive prominent properties of the arrival time probability density. Specifically, we establish the scaling properties of the central moments, analyze the behavior of the probability density for short, long, and intermediate distances. In order to quantify the deviation of the arrival time distribution from a Gaussian shape, we evaluate the skewness and the kurtosis.