Geometric scattering of a scalar particle moving on a curved surface in the presence of point defects

Abstract

A nonrelativistic scalar particle that is constrained to move on an asymptotically flat curved surface undergoes a geometric scattering that is sensitive to the mean and Gaussian curvatures of the surface. A careful study of possible realizations of this phenomenon in typical condensed matter systems requires dealing with the presence of defects. We examine the effect of delta-function point defects residing on a curved surface $S$. In particular, we solve the scattering problem for a multi-delta-function potential in plane, which requires a proper regularization of divergent terms entering its scattering amplitude, and include the effects of nontrivial geometry of $S$ by treating it as a perturbation of the plane. This allows us to obtain analytic expressions for the geometric scattering amplitude for a surface consisting of one or more Gaussian bumps. In general the presence of the delta-function defects enhances the geometric scattering effects.

arXiv comment26 pages, 18 figures, accepted for publication in Annals of Physics

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Cited by in corpus (9)

• Fundamental transfer matrix and dynamical formulation of stationary scattering in two and three dimensions
• Quantum Scattering of Spinless Particles in Riemannian Manifolds
• Singularity-free treatment of delta-function point scatterers in two dimensions and its conceptual implications
• Scattering by a collection of $\delta$-function point and parallel line defects in two dimensions
• Comment on "Scattering of light by a parity-time-symmetric dipole beyond the first Born approximation"
• Geometric scattering in the presence of line defects
• Sphere on a plane: Two-dimensional scattering from a finite curved region
• Introducing a general method for solving electromagnetic radiation problem in an arbitrary linear medium
• Renormalization of multi-delta-function point scatterers in two and three dimensions, the coincidence-limit problem, and its resolution