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arXiv · 1905.01808

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

Hai Viet Bui·Ali Mostafazadeh
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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.

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Hai Viet Bui, Ali Mostafazadeh. 2019-05-02. Geometric scattering of a scalar particle moving on a curved surface in the presence of point defects. https://doi.org/10.1016/j.aop.2019.05.001

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