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TT: Fachverband Tiefe Temperaturen

TT 92: Transport – Poster

TT 92.14: Poster

Donnerstag, 12. März 2026, 18:00–20:00, P4

Curvature, Torsion, and Non-Metricity in the Continuum Theory of Lattice Defects — •Marvin Henke and Nikodem Szpak — Fakultät für Physik, Universität Duisburg- Essen, Duisburg, Germany

The continuum theory of lattice defects provides a tractable mesoscale framework for electron transport, circumventing microscopic complexity. It maps dislocations and disclinations onto curvature and torsion within an effective Riemann-Cartan geometry. The equivalence of the two latter concepts is an ongoing debate in General Relativity. Motivated by two-dimensional systems, like graphene, we investigate the mapping of metric-induced curvature onto torsion while preserving physical aspects of the dynamics. Among them, a crucial problem with the (eigen)time scaling along the trajectories of (quasi)particles appears. Our approach to solve this problem lies in the relaxation on the standard metric compatibility condition, which introduces the non-metricity tensor as an additional geometrical object, thus opening a new opportunity to discuss deep problems of differential geometry in the context of real physical systems.

Keywords: continuum theory of defects; differential geometry; curved space