几何散射：无自旋粒子在渐近平坦嵌入表面上运动的情况
Scattering due to geometry: The case of a spinless particle moving on an asymptotically flat embedded surface
摘要：
一个在曲面上自由运动的非相对论量子力学粒子，通过与拉普拉斯-贝尔特拉米算子成比例的哈密顿量的动力学部分和一个几何势（表面平均曲率和高斯曲率的线性组合），感受到曲面的非平凡几何的影响。这些项的系数不能由量子力学的一般原理唯一确定，而是进入各种物理量的计算中。我们研究了它们对运动在渐近平坦嵌入表面上的标量粒子的几何散射的贡献。特别是，考虑到实验实现的几何散射在一个低密度的电子气上形成的凹凸表面的可能性，我们确定的散射振幅的曲率系数的任意选择的表面与全球或局部圆柱对称。我们还研究了违反这种对称性的扰动的影响，并考虑涉及凹凸表面形成一个晶格。
英文摘要：
A nonrelativistic quantum mechanical particle moving freely on a curved surface feels the effect of the nontrivial geometry of the surface through the kinetic part of the Hamiltonian, which is proportional to the Laplace-Beltrami operator, and a geometric potential, which is a linear combination of the mean and Gaussian curvatures of the surface. The coefficients of these terms cannot be uniquely determined by general principles of quantum mechanics but enter the calculation of various physical quantities. We examine their contribution to the geometric scattering of a scalar particle moving on an asymptotically flat embedded surface. In particular, having in mind the possibility of an experimental realization of the geometric scattering in a low density electron gas formed on a bumped surface, we determine the scattering amplitude for arbitrary choices of the curvature coefficients for a surface with global or local cylindrical symmetry. We also examine the effect of perturbations that violate this symmetry and consider surfaces involving bumps that form a lattice.
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