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Mathematical Physics

arXiv:2207.08612 (math-ph)
[Submitted on 18 Jul 2022 (v1), last revised 10 Feb 2023 (this version, v2)]

Title:Winding Number Statistics for Chiral Random Matrices: Averaging Ratios of Determinants with Parametric Dependence

Authors:Nico Hahn, Mario Kieburg, Omri Gat, Thomas Guhr
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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.
Subjects: Mathematical Physics (math-ph); Disordered Systems and Neural Networks (cond-mat.dis-nn)
Cite as: arXiv:2207.08612 [math-ph]
  (or arXiv:2207.08612v2 [math-ph] for this version)
  https://doi.org/10.48550/arXiv.2207.08612
Journal reference: J. Math. Phys. 64, 021901 (2023)
Related DOI: https://doi.org/10.1063/5.0112423

Submission history

From: Nico Hahn [view email]
[v1] Mon, 18 Jul 2022 13:59:13 UTC (386 KB)
[v2] Fri, 10 Feb 2023 13:26:07 UTC (378 KB)
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