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Updated: Feb 26, 2026

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids
Published on: May 27, 2020
GOE-GUE-Poisson transitions in the nearest-neighbor spacing distribution of magnetoexcitons
Frank Schweiner1, Jörg Main1, Günter Wunner1
1Institut für Theoretische Physik 1, Universität Stuttgart, 70550 Stuttgart, Germany.
Abstract:
Recent investigations on the Hamiltonian of excitons by Schweiner et al.. [Phys. Rev. Lett. 118, 046401 (2017)]PRLTAO0031-900710.1103/PhysRevLett.118.046401 revealed that the combined presence of a cubic band structure and external fields breaks all antiunitary symmetries. The nearest-neighbor spacing distribution of magnetoexcitons can exhibit Poissonian statistics, the statistics of a Gaussian orthogonal ensemble (GOE), or a Gaussian unitary ensemble (GUE) depending on the system parameters. Hence, magnetoexcitons are an ideal system to investigate the transitions between these statistics. Here we investigate the transitions between GOE and GUE statistics and between Poissonian and GUE statistics by changing the angle of the magnetic field with respect to the crystal lattice and by changing the scaled energy known from the hydrogen atom in external fields. Comparing our results with analytical formulas for these transitions derived with random matrix theory, we obtain a very good agreement and thus confirm the Wigner surmise for the exciton system.
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