### 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.

Original language | English (US) |
---|---|

Pages (from-to) | 228-249 |

Number of pages | 22 |

Journal | Annals of Physics |

Volume | 407 |

DOIs | |

State | Published - Aug 2019 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Annals of Physics*,

*407*, 228-249. https://doi.org/10.1016/j.aop.2019.05.001

**Geometric scattering of a scalar particle moving on a curved surface in the presence of point defects.** / Bui, Hai Viet; Mostafazadeh, Ali.

Research output: Contribution to journal › Article

*Annals of Physics*, vol. 407, pp. 228-249. https://doi.org/10.1016/j.aop.2019.05.001

}

TY - JOUR

T1 - Geometric scattering of a scalar particle moving on a curved surface in the presence of point defects

AU - Bui, Hai Viet

AU - Mostafazadeh, Ali

PY - 2019/8

Y1 - 2019/8

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85066234402&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85066234402&partnerID=8YFLogxK

U2 - 10.1016/j.aop.2019.05.001

DO - 10.1016/j.aop.2019.05.001

M3 - Article

AN - SCOPUS:85066234402

VL - 407

SP - 228

EP - 249

JO - Annals of Physics

JF - Annals of Physics

SN - 0003-4916

ER -