Related Experiment Video
Updated: May 18, 2026

Stimulated Stokes and Antistokes Raman Scattering in Microspherical Whispering Gallery Mode Resonators
Published on: April 4, 2016
Wigner surmise for mixed symmetry classes in random matrix theory
Sebastian Schierenberg1, Falk Bruckmann, Tilo Wettig
1Institute for Theoretical Physics, University of Regensburg, 93040 Regensburg, Germany.
Abstract:
We consider the nearest-neighbor spacing distributions of mixed random matrix ensembles interpolating between different symmetry classes or between integrable and nonintegrable systems. We derive analytical formulas for the spacing distributions of 2×2 or 4×4 matrices and show numerically that they provide very good approximations for those of random matrices with large dimension. This generalizes the Wigner surmise, which is valid for pure ensembles that are recovered as limits of the mixed ensembles. We show how the coupling parameters of small and large matrices must be matched depending on the local eigenvalue density.
Related Concept Videos
Symmetry in Maxwell's Equations
Symmetry Elements in a Crystal
Gauss's Law: Planar Symmetry
Gauss's Law: Spherical Symmetry
The Pauli Exclusion Principle
Gauss's Law: Cylindrical Symmetry
