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Universality Emerging in a Universality: Derivation of the Ericson Transition in Stochastic Quantum Scattering and Experimental Validation

Simon Köhnes1,*, Jiongning Che2,†, Barbara Dietz2,3,‡,§, and Thomas Guhr1,║

  • *Contact author: simon.koehnes@uni-due.de
  • †Present address: Yangtze Delta Region Institute, University of Electronic Science and Technology of China, Huzhou, China.
  • ‡Contact author: bdietzp@gmail.com
  • §Present address: Max-Planck Institute for the Physics of Complex Systems and TU Dresden, Dresden, Germany.
  • ║Contact author: thomas.guhr@uni-due.de
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Phys. Rev. Lett. 137, 050403 – Published 29 July, 2026

DOI: https://doi.org/10.1103/3gvv-2hq6

Abstract

At lower energies, the resonances in scattering experiments are often isolated. In quantum chaotic many-body, disordered, or generically stochastic systems, the resonances overlap at larger energies. Eventually, the Ericson regime is reached in which the cross section behaves like a random function. The scattering-matrix elements then follow a universal Gaussian distribution. For more than 60 years, the emergence of this robust additional universal behavior on top of the universal system stochasticity has awaited a concise analytical treatment. We derive the transition to the Ericson regime in the universal Heidelberg approach and prove the universal Gaussian distribution by a proper asymptotic expansion. We also obtain explicit formulas for the moments and for the cross-section distribution. We compare with microwave experiments and numerical simulations.

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Phys. Rev. Lett. 137, 050403– Published 29 July, 2026
  • Received 2 April 2025
  • Revised 27 March 2026
  • Accepted 22 June 2026
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