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

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.