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

Hai Viet Bui, Ali Mostafazadeh

Research output: Contribution to journalArticle


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.

Original languageEnglish (US)
Pages (from-to)228-249
Number of pages22
JournalAnnals of Physics
StatePublished - Aug 2019
Externally publishedYes


ASJC Scopus subject areas

  • Physics and Astronomy(all)

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