近日，德国马丁路德·哈勒维腾贝格大学的Benjamin Schwager课题组取得一项新进展。经过不懈努力，他们探究了黎曼流形中无自旋粒子的量子散射。相关研究成果已于2023年6月6日在国际知名学术期刊《物理评论A》上发表。
该研究团队提出了一个约束非相对论粒子在二维空间中进行量子散射的框架。当运动流形具有局部曲率调制时，散射发生在新出现的几何势和度规张量场中。通过理论分析和完全数值模拟，研究人员确定几何势是低能散射的主要来源，而曲空间的度规张量场则主导了高能衍射。与平坦空间相比，微扰方法的适用范围存在重要差异，这一点通过使用有限元和边界元方法进行完全数值模拟得到了证实。
以引力透镜效应为例，研究人员考虑了一个高斯形状的凹陷。实验上，该设置可以通过几何设计的二维材料来实现。
据介绍，量子力学对底层空间的几何结构非常敏感。
附：英文原文
Title: Quantum scattering of spinless particles in Riemannian manifolds
Author: Lars Meschede, Benjamin Schwager, Dominik Schulz, Jamal Berakdar
Issue&Volume: 2023/06/06
Abstract: Quantum mechanics is sensitive to the geometry of the underlying space. Here we present a framework for quantum scattering of a nonrelativistic particle confined to a two-dimensional space. When the motion manifold hosts localized curvature modulations, scattering occurs from an emergent geometric potential and the metric tensor field. Analytical and full numerical simulations identify the geometric potential as the primary source for low-energy scattering, while the metric tensor field of the curved space governs high-energy diffraction. Compared to flat spaces, important differences in the validity range of perturbation approaches are found and demonstrated by full numerical simulations using combined finite element and boundary element methods. As an illustration, we consider a Gaussian-shaped dent leading to effects known as gravitational lensing. Experimentally, the considered setup is realizable based on geometrically engineered two-dimensional materials.
DOI: 10.1103/PhysRevA.107.062806
Source: https://journals.aps.org/pra/abstract/10.1103/PhysRevA.107.062806
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