Quantum motion of a spinless particle in curved space: A viewpoint of scattering theory

TL;DR

This paper investigates how curvature in a surface influences the quantum scattering behavior of a spinless charged particle, revealing that curvature induces bound states and modifies scattering properties.

Contribution

It provides a detailed analysis of curvature effects on quantum scattering, including phase shifts, S-matrix, and bound states, using self-adjoint extension theory.

Findings

Curvature induces bound states in the scattering process.

Scattering amplitude depends on the surface's curvature and energy.

Curvature effects are responsible for additional scattering phenomena.

Abstract

In this work, we study the scattering of a spinless charged particle constrained to move on a curved surface in the presence of the Aharonov-Bohm potential. We begin with the equations of motion for the surface and transverse dynamics previously obtained in the literature (Ferrari G. and Cuoghi G., Phys. Rev. Lett. \textbf{100}, 230403 (2008)) and describe the surface with non-trivial curvature in terms of linear defects such as dislocations and disclinations. Expressions for the modified phase shift, S--matrix and scattering amplitude are determined by applying a suitable boundary condition at the origin, which comes from the self-adjoint extension theory. We also discuss the presence of a bound state obtained from the pole of the S--matrix. Finally, we claim that the bound state, the additional scattering and the dependence of the scattering amplitude with energy are solely due to the curvature effects.