Quantum Scattering of Spinless Particles in Riemannian Manifolds

• URL: http://arxiv.org/abs/2402.10564v1
• Date: Fri, 16 Feb 2024 10:50:50 GMT
• Title: Quantum Scattering of Spinless Particles in Riemannian Manifolds
• Authors: Lars Meschede, Benjamin Schwager, Dominik Schulz, Jamal Berakdar
• Abstract summary: Quantum mechanics is sensitive to the geometry of the underlying space. We present a framework for quantum scattering of a non-relativistic particle confined to a two-dimensional space.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Quantum mechanics is sensitive to the geometry of the underlying space. Here, we present a framework for quantum scattering of a non-relativistic 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 2D materials.

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