Wigner surmise for Hermitian and non-Hermitian chiral random matrices
We use the idea of a Wigner surmise to compute approximate distributions of the first eigenvalue in chiral random matrix theory, for both real and complex eigenvalues. Testing against known results for zero and maximal non-Hermiticity in the microscopic large-N limit, we find an excellent agreement...
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| Main Authors: | , , , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
3 December 2009
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| In: |
Physical review. E, Statistical, nonlinear, and soft matter physics
Year: 2009, Volume: 80, Issue: 6, Pages: 1-4 |
| ISSN: | 1550-2376 |
| DOI: | 10.1103/PhysRevE.80.065201 |
| Online Access: | Verlag, Volltext: http://dx.doi.org/10.1103/PhysRevE.80.065201 Verlag, Volltext: https://link.aps.org/doi/10.1103/PhysRevE.80.065201 
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| Author Notes: | G. Akemann, E. Bittner, M.J. Phillips, and L. Shifrin |
| Summary: | We use the idea of a Wigner surmise to compute approximate distributions of the first eigenvalue in chiral random matrix theory, for both real and complex eigenvalues. Testing against known results for zero and maximal non-Hermiticity in the microscopic large-N limit, we find an excellent agreement valid for a small number of exact zero eigenvalues. Compact expressions are derived for real eigenvalues in the orthogonal and symplectic classes and at intermediate non-Hermiticity for the unitary and symplectic classes. Such individual Dirac eigenvalue distributions are a useful tool in lattice gauge theory, and we illustrate this by showing that our results can describe data from two-color quantum chromodynamics simulations with chemical potential in the symplectic class. |
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| Item Description: | Gesehen am 13.11.2017 |
| Physical Description: | Online Resource |
| ISSN: | 1550-2376 |
| DOI: | 10.1103/PhysRevE.80.065201 |