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This study provides the first complete analytical derivation of the Ericson regime transition in quantum scattering, a phenomenon where scattering cross-sections behave randomly at high energies in chaotic quantum systems. The researchers prove that scattering-matrix elements follow a universal Gaussian distribution using the Heidelberg approach and derive explicit formulas for distribution moments. The theoretical predictions are validated through both microwave experiments and numerical simulations.
Why it matters
This work resolves a sixty-year-old theoretical problem in quantum scattering theory, providing a rigorous mathematical foundation for understanding energy-dependent transitions in complex quantum systems. The results have implications for nuclear physics, quantum chaos studies, and the design of microwave devices where scattering processes in complex environments are important.
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⚠️ Preprint – Noch nicht peer-reviewed
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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 sixty 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 formulae for the moments of the distributions. We compare with microwave experiments and numerical simulations.