Geometric scattering in the presence of line defects

TL;DR

This paper investigates how line defects on a curved surface influence geometric scattering of a scalar particle, revealing that such defects amplify scattering effects and can help resolve ambiguities in the quantum Hamiltonian's curvature coefficients.

Contribution

It provides a detailed analysis of geometric scattering with line defects, showing how these defects enhance scattering effects and can clarify Hamiltonian ambiguity issues.

Findings

Line defects amplify geometric scattering on curved surfaces.

Scattering vanishes on flat surfaces except at specific angles.

Centering the bump between line defects maximizes amplification.

Abstract

A non-relativistic scalar particle moving on a curved surface undergoes a geometric scattering whose behavior is sensitive to the theoretically ambiguous values of the intrinsic and extrinsic curvature coefficients entering the expression for the quantum Hamiltonian operator. This suggests using the scattering data to settle the ambiguity in the definition of the Hamiltonian. It has recently been shown that the inclusion of point defects on the surface enhances the geometric scattering effects. We perform a detailed study of the geometric scattering phenomenon in the presence of line defects for the case that the particle is confined to move on a Gaussian bump and the defect(s) are modeled by delta-function potentials supported on a line or a set of parallel lines normal to the scattering axis. In contrast to a surface having point defects, the scattering phenomenon associated with this system is generically geometric in nature in the sense that for a flat surface the scattering amplitude vanishes for all scattering angles $\theta$ except $\theta=\theta_0$ and $\pi-\theta_0$, where $\theta_0$ is the angle of incidence. We show that the presence of the line defects amplifies the geometric scattering due to the Gaussian bump. This amplification effect is particularly strong when the center of the bump is placed between two line defects.