Berlin 2024 – scientific programme

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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik

MP 3: Quantum Dynamics

MP 3.6: Talk

Monday, March 18, 2024, 17:10–17:30, HL 001

Quantum Scattering upon Local Deformations in Configuration Space — •Benjamin Schwager, Lars Meschede, and Jamal Berakdar — MLU Halle-Wittenberg, Halle (Saale), Germany

When a quantum particle is subjected to spatial constraints, its dynamics have to be modelled based on a configuration space that is a more general Riemannian manifold than Euclidean space. The resulting effective quantum wave equations contain correction terms in dependence of the geometric properties of this space. We apply the confinement potential approach to the Schrödinger equation to obtain an effective wave equation in reduced dimensions, and show that position-dependent modulations of the geometric invariants and the metric tensor cause lower-dimensional scattering events. It is found that theire characteristics differ significantly from the case of more familiar potential scattering. Furthermore, we present consequences for transport properties.

Keywords: spatial constraints; dimensional reduction; Riemannian geometry; geometry-induced effects; scattering theory