A Universality Emerging in a Universality: Derivation of the Ericson Transition in Stochastic Quantum Scattering and Experimental Validation
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| Format: | Preprint |
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2026
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| _version_ | 1866914387849117696 |
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| author | Köhnes, Simon Che, Jiongning Dietz, Barbara Guhr, Thomas |
| author_facet | Köhnes, Simon Che, Jiongning Dietz, Barbara Guhr, Thomas |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_12068 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Universality Emerging in a Universality: Derivation of the Ericson Transition in Stochastic Quantum Scattering and Experimental Validation Köhnes, Simon Che, Jiongning Dietz, Barbara Guhr, Thomas Statistical Mechanics Nuclear Theory Atomic Physics 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. |
| title | A Universality Emerging in a Universality: Derivation of the Ericson Transition in Stochastic Quantum Scattering and Experimental Validation |
| topic | Statistical Mechanics Nuclear Theory Atomic Physics |
| url | https://arxiv.org/abs/2603.12068 |