Regensburg 2025 – scientific programme

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HL: Fachverband Halbleiterphysik

HL 38: Nanomechanical systems (joint session HL/TT)

HL 38.2: Talk

Wednesday, March 19, 2025, 15:15–15:30, H17

Quantum Mechanics in Two-Dimensional Dynamic Spaces — •Benjamin Schwager and Jamal Berakdar — Martin-Luther-Universität Halle-Wittenberg, Halle (Saale), Germany

In the study of systems with reduced dimensions one encounters quantum particles under spatial constraints. Their dynamics have to be modeled based on a configuration space that is a Riemannian manifold, in general, and the resulting quantum wave equations contain correction terms in dependence of its geometric properties. We consider particles which are confined to a flexible thin material shell by studying the Schrödinger equation on moving domains. The model assumes a static observer and couples the deformation dynamics of the material to the quantum dynamics it hosts via additional potential fields. Effects caused by the interplay of geometry and the temporal evolution of the underlying configuration space will be discussed.

Keywords: quantum mechanics under consraints; Riemannian geometry; Schrödinger equation on moving domains; thin shells