Regensburg 2025 – scientific programme

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MA: Fachverband Magnetismus

MA 41: Poster III

MA 41.8: Poster

Thursday, March 20, 2025, 15:00–17:30, P3

Pauli-Equation on Riemannian Manifolds — •Johann Posanski, Benjamin Schwager, and Jamal Berakdar — Marthin-Luther-Universität Halle-Wittenberg Institut für Physik

Describing the behavior of quantum systems under geometric constraints is of relevance both for research in the foundations of physics and in applied fields, such as the development of designer materials. Implementing the restriction of a quantum particle to a Riemannian manifold with an explicit confining potential provides an effective description of the reduced quantum dynamics and implies a potential-like term dependent on the geometric invariants of the space. Expanding this formalism to spin-1/2 particles, such as electrons, is an active area of research. In this work, the dynamics of non-relativistic spin-1/2 particles on a two-dimensional Riemannian manifold embedded in three-dimensional Euclidean space are derived. We find that the spin degree of freedom is unaffected by real-space constraints and the tangent Pauli equation fully describes the spinor dynamics when the whole structure is exposed to an electromagnetic field. The Zeeman energy is found to be unaffected by the confinement and remains gauge-invariant.

Keywords: QM on Manifolds; Pauli-Equation on Manifolds; Spin-1/2 particles on Manifolds; Confining Potential approach (CPA); Spin-Coupling