Erlangen 2026 – scientific programme

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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik

MP 9: Geometry, Black Holes, Universality

MP 9.4: Talk

Thursday, March 19, 2026, 12:00–12:15, KH 02.013

A New Universality Emerging in the Generic Approach to Stochastic Quantum Scattering — •Simon Köhnes and Thomas Guhr — Universität Duisburg-Essen, Duisburg, Deutschland

Scattering theory is indispensable to understand a variety of systems ranging from nuclei and atoms to systems in mesoscopic and condensed matter physics, but also to wireless communication. These systems often exhibit chaotic dynamics in a broad sense which prompted generic stochastic approaches. Recently we succeeded in deriving the distributions for off-diagonal scattering matrix elements and cross sections by using Random Matrix Theory and Supersymmetry. We arrive at integrals over Goldstone modes, more precisely over a coset supermanifold. These results now facilitate to prove a 60 year old conjecture: Ericson argued that the mentioned distributions become Gaussian or exponential, respectively, in the regime of strongly overlapping resonances. Our proof is based on an asymptotic expansion which we carry out after a proper reparameterization of the multidimensional integration manifold.

Keywords: Random Matrix Theory; Supersymmetry; Quantum Chaos; Chaotic Scattering