Spectral rigidity of non-Hermitian symmetric random matrices near the Anderson transition

We study the spectral rigidity of the non-Hermitian analog of the Anderson model suggested by Tzortzakakis, Makris, and Economou (TME). This is a L×L×L tightly bound cubic lattice, where both real and imaginary parts of onsite energies are independent random variables uniformly distributed between −...

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Bibliographic Details
Published in:Physical review. B 2020-08, Vol.102 (6), p.1, Article 064212
Main Authors: Huang, Yi, Shklovskii, B. I.
Format: Article
Language:English
Subjects:
Cubic lattice
Eigenvalues
Energy bands
Energy levels
Independent variables
Matrix methods
Random variables
Rigidity
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Summary:We study the spectral rigidity of the non-Hermitian analog of the Anderson model suggested by Tzortzakakis, Makris, and Economou (TME). This is a L×L×L tightly bound cubic lattice, where both real and imaginary parts of onsite energies are independent random variables uniformly distributed between −W/2 and W/2. The TME model may be used to describe a random laser. In a recent paper we proved that this model has the Anderson transition at W=Wc≃6 in three dimension. Here we numerically diagonalize TME L×L×L cubic lattice matrices and calculate the number variance of eigenvalues in a disk of their complex plane. We show that on the metallic side W
ISSN:2469-9950
2469-9969
DOI:10.1103/PhysRevB.102.064212