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

TL;DR

This paper derives the transition to the Ericson regime in quantum scattering, demonstrating the universal Gaussian distribution of scattering matrix elements and validating the theory with experiments and simulations.

Contribution

It provides the first concise analytical derivation of the Ericson transition and universal Gaussian distribution in stochastic quantum scattering.

Findings

Derived explicit formulas for moments of the distributions.

Validated theoretical predictions with microwave experiments.

Confirmed the universal Gaussian behavior through numerical simulations.

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 awaits 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.