Statistical Topology—Distribution and Density Correlations of Winding Numbers in Chiral Systems
Abstract
1. Introductory Remarks
2. Winding Numbers and Chirality
2.1. A Simple Topological Invariant in Complex Analysis
2.2. Kitaev Chain and Winding Numbers
2.3. Chirality, Random Winding Numbers and Modelling Aspects
2.4. Connections to Quantum Chromodynamics and Condensed Matter Physics
3. Formulation of the Problem and Mathematical Setup
3.1. Chiral Random Matrix Ensembles with Parametric Dependence
3.2. Statistical Quantities Considered
3.3. Mapping a Topological to a Spectral Problem
4. Results
4.1. Winding Number Correlators in the Chiral Unitary Case
4.2. Winding Number Distribution
4.3. Aspects of Universality
4.4. Generators in the Chiral Unitary and Symplectic Cases
5. Discussion and Conclusions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Abbreviations
RMT | Random Matrix Theory |
QCD | Quantum Chromodynamics |
chGUE | chiral Gaussian Unitary Ensemble |
chGSE | chiral Gaussian Symplectic Ensemble |
permutation group of N objects |
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Guhr, T. Statistical Topology—Distribution and Density Correlations of Winding Numbers in Chiral Systems. Entropy 2023, 25, 383. https://doi.org/10.3390/e25020383
Guhr T. Statistical Topology—Distribution and Density Correlations of Winding Numbers in Chiral Systems. Entropy. 2023; 25(2):383. https://doi.org/10.3390/e25020383
Chicago/Turabian StyleGuhr, Thomas. 2023. "Statistical Topology—Distribution and Density Correlations of Winding Numbers in Chiral Systems" Entropy 25, no. 2: 383. https://doi.org/10.3390/e25020383
APA StyleGuhr, T. (2023). Statistical Topology—Distribution and Density Correlations of Winding Numbers in Chiral Systems. Entropy, 25(2), 383. https://doi.org/10.3390/e25020383