Euclidean random matrices and their applications in physics
A. Goetschy, S.E. Skipetrov
TL;DR
This paper reviews the theory of Euclidean random matrices, emphasizing eigenvalue densities, and explores their applications across physics disciplines like condensed matter, optics, and quantum chaos.
Contribution
It provides a comprehensive overview of Euclidean random matrices, connecting their spectral properties to various physical phenomena and related random matrix ensembles.
Findings
Eigenvalue density characterizations for Hermitian and non-Hermitian matrices.
Connections established between Euclidean random matrices and standard ensembles.
Applications demonstrated in condensed matter, optics, and quantum chaos.
Abstract
We review the state of the art of the theory of Euclidean random matrices, focusing on the density of their eigenvalues. Both Hermitian and non-Hermitian matrices are considered and links with simpler, standard random matrix ensembles are established. We discuss applications of Euclidean random matrices to contemporary problems in condensed matter physics, optics, and quantum chaos.
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Taxonomy
TopicsRandom Matrices and Applications · Random lasers and scattering media · advanced mathematical theories