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PreprintarXiv licencearXiv

The Ericson Transition in Time-Reversal Invariant Systems: Orthogonally Invariant Hamiltonians

  • Simon Köhnes
  • Thomas Guhr
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Abstract

We investigate the distributions of off-diagonal scattering matrix elements and cross-sections in the Ericson regime for systems that are time-reversal and rotationally invariant. In previous works, we developed techniques to analyze the Ericson transition by means of asymptotic expansions in the cases of unitarily and symplectically invariant Hamiltonians. Here, we prove that Gaussian and exponential behavior is found as the leading-order term of an asymptotic expansion of those distributions also in the orthogonal case, which is often the relevant one for analyzing experiments. Moreover, we derive the subleading-order term and compare with numerical simulations. Finally, we discuss similarities and differences of the Ericson transition for all three Wigner-Dyson classes.

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Cite

BibTeXRIS
BibTeX
@misc{kohnes2026ericson,
  title = {{The Ericson Transition in Time-Reversal Invariant Systems: Orthogonally Invariant Hamiltonians}},
  author = {Simon Köhnes and Thomas Guhr},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.25103},
  eprint = {2610.25103},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.25103},
}
RIS
TY  - UNPB
TI  - The Ericson Transition in Time-Reversal Invariant Systems: Orthogonally Invariant Hamiltonians
AU  - Simon Köhnes
AU  - Thomas Guhr
PY  - 2026
DA  - 2026/10/18
PB  - arXiv
DO  - 10.48550/arxiv.2610.25103
UR  - https://arxiv.org/abs/2610.25103
AB  - We investigate the distributions of off-diagonal scattering matrix elements and cross-sections in the Ericson regime for systems that are time-reversal and rotationally invariant. In previous works, we developed techniques to analyze the Ericson transition by means of asymptotic expansions in the cases of unitarily and symplectically invariant Hamiltonians. Here, we prove that Gaussian and exponential behavior is found as the leading-order term of an asymptotic expansion of those distributions also in the orthogonal case, which is often the relevant one for analyzing experiments. Moreover, we derive the subleading-order term and compare with numerical simulations. Finally, we discuss similarities and differences of the Ericson transition for all three Wigner-Dyson classes.
ER  -