Geodesics around a dislocation

TL;DR

This paper investigates particle trajectories around a dislocation by solving the Hamilton-Jacobi equation for geodesics in a medium with torsional defects, providing insights into the effects of topological defects.

Contribution

It introduces a perturbative method to solve the Hamilton-Jacobi equation for geodesics around an edge dislocation, advancing understanding of particle motion in defective media.

Findings

Derived the first-order solution for geodesics near a dislocation

Provided a framework for analyzing particle trajectories in topologically defective materials

Enhanced understanding of defect-induced effects on particle motion

Abstract

One method of gaining some insight into the motion of particles in a medium with topological defects (e.g., electrons in a dislocated metal) is to look at the geodesics of the medium around the defect. In this work the Hamilton-Jacobi equation for the geodesics in a continuous medium containing a torsional defect, an edge dislocation, is solved by using perturbation theory to first order in the Burgers vector.