Winding Number Statistics for Chiral Random Matrices: Averaging Ratios of Determinants with Parametric Dependence
Mathematical Physics
2023-02-13 v2 Disordered Systems and Neural Networks
math.MP
Abstract
Topological invariance is a powerful concept in different branches of physics as they are particularly robust under perturbations. We generalize the ideas of computing the statistics of winding numbers for a specific parametric model of the chiral Gaussian Unitary Ensemble to other chiral random matrix ensembles. Especially, we address the two chiral symmetry classes, unitary (AIII) and symplectic (CII), and we analytically compute ensemble averages for ratios of determinants with parametric dependence. To this end, we employ a technique that exhibits reminiscent supersymmetric structures while we never carry out any map to superspace.
Keywords
Cite
@article{arxiv.2207.08612,
title = {Winding Number Statistics for Chiral Random Matrices: Averaging Ratios of Determinants with Parametric Dependence},
author = {Nico Hahn and Mario Kieburg and Omri Gat and Thomas Guhr},
journal= {arXiv preprint arXiv:2207.08612},
year = {2023}
}