Singularities in the spectra of random matrices

DOI10.1063/1.531686zbMath0864.15012OpenAlexW1983848612MaRDI QIDQ5284724

Paul N. Walker, María José Sánchez, Michael H. F. Wilkinson

Publication date: 8 June 1997

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.531686

zbMATH Keywords

disordered systemsHamiltonianscorrelation functionsrandom matrix modelsquantum mechanical equationsdensities of singularities

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics (82B44) Eigenvalues, singular values, and eigenvectors (15A18) Random matrices (algebraic aspects) (15B52)

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Takagi Factorization of Matrices Depending on Parameters and Locating Degeneracies of Singular Values ⋮ Hermitian matrices depending on three parameters: Coalescing eigenvalues ⋮ Coalescing points for eigenvalues of banded matrices depending on parameters with application to banded random matrix functions ⋮ Hermitian matrices of three parameters: perturbing coalescing eigenvalues and a numerical method ⋮ Continuous Decompositions and Coalescing Eigenvalues for Matrices Depending on Parameters

Cites Work

• Diabolical points in the spectra of triangles
• Jacobi Polynomials Associated with Selberg Integrals
• Statistical properties of parameter-dependent classically chaotic quantum systems
• Non-adiabatic crossing of energy levels
• Exact distribution of eigenvalue curvatures of chaotic quantum systems
• Nuclear Constitution and the Interpretation of Fission Phenomena
• Mathematical Analysis of Random Noise