Quantum Scattering of Spinless Particles in Riemannian Manifolds
arXiv:2402.10564 · doi:10.1103/PhysRevA.107.062806
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.
arXiv comment15 pages, 5 figures
References in corpus (26)
- Weak Gravitational Lensing
- Construction of arbitrary order finite element degree-of-freedom maps on polygonal and polyhedral cell meshes
- Quantum mechanics on curved 2D systems with electric and magnetic fields
- Dynamics and efficient conversion of excitons to trions in non-uniformly strained monolayer WS
- Quantum Mechanics on Manifolds Embedded in Euclidean Space
- Observation of ultracold atomic bubbles in orbital microgravity
- Geometric potential and transport in photonic topological crystals
- Quantizing Constrained Systems: New Perspectives
- Edge states and topological insulating phases generated by curving a nanowire with Rashba spin-orbit coupling
- A Complete Perturbative Expansion for Constrained Quantum Dynamics
- Absence of anomalous interactions in the quantum theory of constrained charged particles in presence of electrical currents
- Curvature-induced geometric potential in strain-driven nanostructures
- Classical and quantum dynamics of confined test particles in brane gravity
- Quantum mechanics of a constrained electrically charged particle in the presence of electric currents
- Pseudo-magnetic field and effective spin-orbit interaction for a spin-1/2 particle confined to a curved surface
- Supersymmetry and the Atiyah-Singer Index Theorem I: Peierls Brackets, Green's Functions, and a Supersymmetric Proof of the Index Theorem
- Potential Scattering on a Spherical Surface
- Two dimensional dipolar scattering with a tilt
- Anisotropic quantum scattering in two dimensions
- Scalar Curvature Factor in the Schroedinger Equation and Scattering on a Curved Surface
- Effective quantum dynamics in curved thin-layer system with inhomogeneous confinement
- Geometric scattering of a scalar particle moving on a curved surface in the presence of point defects
- Supersymmetry and the Atiyah-Singer Index Theorem II: The Scalar Curvature Factor in the Schr{\" o}dinger Equation
- Scattering due to geometry: The case of a spinless particle moving on an asymptotically flat embedded surface
- Magnetic and geometric effects on the electronic transport of metallic nanotubes
- Sphere on a plane: Two-dimensional scattering from a finite curved region