Influence of Time Reversal Invariance Breaking on the Distribution of Off-Diagonal Scattering Matrix Elements and Cross Sections
Abstract
Scattering theory is a key tool for the investigation of quantum systems. Universal approaches are of interest, particularly in the framework of Random Matrix Theory. Dyson's Threefold way classifies systems according to their behavior under time reversal. In these three cases the distribution of off-diagonal scattering matrix elements and cross sections were recently calculated. However, in many applications systems neither display full nor fully broken time reversal invariance, such as systems in tuneable external magnetic fields. The study of these systems has a long history, also in Random Matrix Theory. We investigate the influence of time reversal invariance breaking on the universal behavior of the mentioned distributions. Using supersymmetry we succeed in deriving exact expressions for the distribution of off-diagonal scattering matrix elements and cross sections in systems with half-integer or integer/no spin in the absence of further symmetries. We find that the distributions are symmetric while the scattering matrix elements are not. Furthermore, our results might considerably facilitate the data analysis of time reversal invariance breaking.
Related
- Correction to the article "Global well-posedness and scattering in weighted space for nonlinear Schrödinger equations below the Strauss exponent without gauge-invariance"
- Threshold for the existence of scattering states for inhomogeneous nonlinear Schrödinger equations without gauge invariance
- Breaking the Spin Degeneracy for Distributions of Off-Diagonal Scattering Matrix Elements in the Case of Symplectic Symmetry
- Permutation invariance in last-passage percolation and the distribution of the Busemann process
- Distribution of Scattering Matrix Elements in the case of Symplectic Symmetry
BibTeX
@misc{gluth2026influence,
title = {{Influence of Time Reversal Invariance Breaking on the Distribution of Off-Diagonal Scattering Matrix Elements and Cross Sections}},
author = {Nils Gluth and Ahmed Aldabag and Thomas Guhr},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.37724},
eprint = {2609.37724},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.37724},
}
RIS
TY - UNPB
TI - Influence of Time Reversal Invariance Breaking on the Distribution of Off-Diagonal Scattering Matrix Elements and Cross Sections
AU - Nils Gluth
AU - Ahmed Aldabag
AU - Thomas Guhr
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.37724
UR - https://arxiv.org/abs/2609.37724
AB - Scattering theory is a key tool for the investigation of quantum systems. Universal approaches are of interest, particularly in the framework of Random Matrix Theory. Dyson's Threefold way classifies systems according to their behavior under time reversal. In these three cases the distribution of off-diagonal scattering matrix elements and cross sections were recently calculated. However, in many applications systems neither display full nor fully broken time reversal invariance, such as systems in tuneable external magnetic fields. The study of these systems has a long history, also in Random Matrix Theory. We investigate the influence of time reversal invariance breaking on the universal behavior of the mentioned distributions. Using supersymmetry we succeed in deriving exact expressions for the distribution of off-diagonal scattering matrix elements and cross sections in systems with half-integer or integer/no spin in the absence of further symmetries. We find that the distributions are symmetric while the scattering matrix elements are not. Furthermore, our results might considerably facilitate the data analysis of time reversal invariance breaking.
ER -