title: Wigner surmise for mixed symmetry classes in random matrix theory.
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.
authors.affiliation: Institute for Theoretical Physics, University of Regensburg, 93040 Regensburg, Germany.
authors.forename: Sebastian
authors.initials: S
authors.lastname: Schierenberg
authors.forename: Falk
authors.initials: F
authors.lastname: Bruckmann
authors.forename: Tilo
authors.initials: T
authors.lastname: Wettig
mesh_terms: D003102:Colloids / Q000737:chemistry*; D003198:Computer Simulation; D008956:Models, Chemical; D015233:Models, Statistical
chemical_list: D003102:Colloids