Distribution of Scattering Matrix Elements in the case of Symplectic Symmetry
Abstract
Scattering theory is at the core of gaining information about most quantum systems. In general, analytic progress is difficult and the investigation of universal features using statistical methods is of interest. Commonly this is carried out within the Heidelberg approach which models the Hamiltonian of the target by a random matrix. Hitherto, such investigations were performed for systems that are effectively spinless or have total angular momentum conservation. In light of recent experimental progress it has become relevant to also investigate systems with half-integer spin. Using supersymmetry, we derive the distribution for the real and imaginary parts of the scattering matrix elements and the corresponding cross sections in the case of symplectic symmetry. These results complete the derivations for Dysons threefold way.
Related
- Breaking the Spin Degeneracy for Distributions of Off-Diagonal Scattering Matrix Elements in the Case of Symplectic Symmetry
- Influence of Time Reversal Invariance Breaking on the Distribution of Off-Diagonal Scattering Matrix Elements and Cross Sections
- Centralizers of elements in the orthogonal, symplectic and unitary groups
- Fractional symplectic Fourier transforms and their actions on function and distribution spaces
- Winding Number Statistics of a Parametric Chiral Symplectic Random Matrix Ensemble
BibTeX
@misc{gluth2026distribution,
title = {{Distribution of Scattering Matrix Elements in the case of Symplectic Symmetry}},
author = {Nils Gluth and Thomas Guhr},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.37696},
eprint = {2609.37696},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.37696},
}
RIS
TY - UNPB
TI - Distribution of Scattering Matrix Elements in the case of Symplectic Symmetry
AU - Nils Gluth
AU - Thomas Guhr
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.37696
UR - https://arxiv.org/abs/2609.37696
AB - Scattering theory is at the core of gaining information about most quantum systems. In general, analytic progress is difficult and the investigation of universal features using statistical methods is of interest. Commonly this is carried out within the Heidelberg approach which models the Hamiltonian of the target by a random matrix. Hitherto, such investigations were performed for systems that are effectively spinless or have total angular momentum conservation. In light of recent experimental progress it has become relevant to also investigate systems with half-integer spin. Using supersymmetry, we derive the distribution for the real and imaginary parts of the scattering matrix elements and the corresponding cross sections in the case of symplectic symmetry. These results complete the derivations for Dysons threefold way.
ER -