Geometric scattering in the presence of line defects
Department of Chemistry and Physics, Augusta University, 1120 15th Street, 30912, Augusta, GA, USA
2 Departments of Mathematics and Physics, Koç University, 34450, Sarıyer, Istanbul, Turkey
3 Department of Physics, Boğaziçi University, 34342, Bebek, Istanbul, Turkey
Accepted: 11 January 2021
Published online: 20 January 2021
A nonrelativistic 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 except and , where 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.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2021