存在线缺陷时的几何散射
Geometric scattering in the presence of line defects
摘要：
一个非相对论标量粒子在曲面上运动时会发生几何散射，其行为对进入量子哈密顿算符表达式的本征和非本征曲率系数的理论模糊值敏感。这表明使用散射数据来解决哈密顿量定义中的模糊性。最近已经表明，在表面上的点缺陷的列入增强的几何散射效应。我们进行了详细的研究的几何散射现象中存在的线缺陷的情况下，粒子被限制到移动的高斯凸块和缺陷（S）的情况下，由δ函数电位支持的线或一组平行线垂直于散射轴。与具有点缺陷的表面相反，与该系统相关联的散射现象在本质上一般是几何的，在这个意义上，对于平坦表面，对于除了$θ=θ_0$和$π-θ_0$之外的所有散射角$θ$，散射振幅为零，其中$θ_0$是入射角。我们表明，线缺陷的存在下，由于高斯凹凸放大的几何散射。当凸块的中心位于两个线缺陷之间时，这种放大效应特别强。
英文摘要：
A non-relativistic 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 $θ$ except $θ=θ_0$ and $π-θ_0$, where $θ_0$ 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.
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