Mainz 2026 – wissenschaftliches Programm

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Q: Fachverband Quantenoptik und Photonik

Q 43: Poster – Quantum Systems

Q 43.15: Poster

Mittwoch, 4. März 2026, 17:00–19:00, Philo 2. OG

Symmetry assignment of few-electron states and their Coulomb splitting on molecular networks — Ludwig Schulz, Anton Bauer, and •Carsten Henkel — Universität Potsdam, Institut für Physik und Astronomie, Germany

We investigate few-electron states on a graph, as a tight-binding model of a small molecule. For rings, the dihedral group provides a complete classification of degeneracies in terms of its irreducible representations (Mulliken symbols) [1]. We sketch a graph-theoretical explanation of energy splittings due to the Coulomb interaction between electrons. Similar arguments are applied to rings with ligands and to (avoided) crossings of Zeeman spectra in a magnetic field. A key technique involves adjacency matrices for many-electron states in the occupation number representation, that encode the hopping of one or more electrons and include signs due to the fermionic symmetry and Peierls phase factors in a magnetic field.

[1] P. Atkins and R. Friedman, Molecular Quantum Mechanics (Oxford Univ Press 2005)

Keywords: many-body system; interacting fermions; point group symmetry