Regensburg 2025 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 45: Quantum Chaos (joint session DY/TT)

DY 45.3: Talk

Friday, March 21, 2025, 12:00–12:15, H37

Solved after 60 years: Exact Derivation of the Ericson Transition in Quantum Chaotic Scattering — •Simon Köhnes and Thomas Guhr — University of Duisburg-Essen, Lotharstr. 1, 47048 Duisburg, Germany

Scattering experiments are the prime source of information on the quantum world. Scattering theory nowadays has numerous applications in various branches of physics and beyond, even including classical wave phenomena. We analyze chaotic scattering systems in the framework of Random Matrix Theory. The distribution of the scattering matrix elements is the key quantity. A strong sign of chaos in complex quantum systems is the Ericson regime of strongly overlapping resonances in which the cross sections exhibit random behavior. We apply the Supersymmetry Method. For the three Wigner-Dyson symmetry classes, we analytically calculate the transition to the Ericson regime, facilitating direct comparison with experimental results. In the course of doing so, we also gather new information on features of the underlying supersymmetric non-linear sigma model.

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