Localization of defects via residence time measures

TL;DR

This paper demonstrates that residence time measures in a one-dimensional random walk can effectively identify the location and properties of a defect site, aiding in the characterization of lattice structures.

Contribution

It introduces a method using residence time measures to detect defect location and properties in a simple random walk model, which was not previously established.

Findings

Residence time correlates with defect properties.

Crossing fraction reveals defect location.

Method accurately identifies defect parameters.

Abstract

We show that residence time measure can be used to identify the geometrical and transmission properties of a defect along a path. The model we study is based on a one--dimensional simple random walk. The sites of the lattice are regular, i.e., the jumping probabilities are the same in each site, except for a site, called \emph{defect}, where the jumping probabilities are different. At each side of the lattice an absorbing site is present. We show that by measuring the fraction of particles crossing the channel and/or the typical time they need to cross it, it is possible to identify the main features of the lattice and of the defect site, namely, the jumping probabilities at regular and at the defect sites and the position of the defect in the lattice.