论文标题
平面上的球：有限弯曲区域的二维散射
Sphere on a plane: Two-dimensional scattering from a finite curved region
论文作者
论文摘要
有效地局限于二维的非相关粒子通常可以在弯曲的表面上移动，从而使动态现象超出了标量电势甚至矢量规范场所能描述的超出内容。在这里，我们考虑了一个简单的分段均匀曲率的情况：粒子在带有球形挤出的平面上移动。根据球体连接到平面的纬度，挤压范围从无限的颠簸到几乎完全接触平面的几乎全球。分段均匀曲率表面上的自由经典运动遵循与速度无关的大地测量学，而量子机械散射取决于能量。我们比较了经典，半古典和完全量子问题，这些问题都是可以解决的，并显示了半古典分析如何用两个经典轨迹之间的干扰来解释复杂的量子差分横截面：平面上的球体充当了一种双重缝隙。
Non-relativistic particles that are effectively confined to two dimensions can in general move on curved surfaces, allowing dynamical phenomena beyond what can be described with scalar potentials or even vector gauge fields. Here we consider a simple case of piecewise uniform curvature: a particle moves on a plane with a spherical extrusion. Depending on the latitude at which the sphere joins the plane, the extrusion can range from an infinitesimal bump to a nearly full sphere that just touches the plane. Free classical motion on this surface of piecewise uniform curvature follows geodesics that are independent of velocity, while quantum mechanical scattering depends on energy. We compare classical, semi-classical, and fully quantum problems, which are all exactly solvable, and show how semi-classical analysis explains the complex quantum differential cross section in terms of interference between two classical trajectories: the sphere on a plane acts as a kind of double slit.
