2023/08/02 by Pete Rigas, Rigas, Pete
Computer Science · Mathematics · Physics and Astronomy · #81V02 #82D02 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Matrix Theory and Algorithms #Quantum optics and atomic interactions #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics #Statistical Mechanics (cond-mat.stat-mech)
paper · pdf · doi:10.48550/arxiv.2308.01842
openalex publication_date 2023/08/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Asymptotically, we analytically derive the form of eigenvectors for two Fisher-Hartwig symbols besides those which were previously investigated in a 2016 work due to Movassagh and Kadanoff, in which the authors characterized the eigenpairs of Toeplitz matrices generated by Fisher-Hartwig symbols with one singularity. To perform such computations, we extend their methods which consists of formulating an eigenvalue problem, obtained by a Wiener-Hopf method, from which a suitable winding number is defined for passing to Fourier space, and introducing a factorization dependent upon the winding number, for other Fisher-Hartwig symbols which have previously been defined in the literature. Following the computations required for the proof after obtaining the asymptotic approximation of the eigenvectors, we provide a table from which eigenvalues of one Fisher-Hartwig symbol for different complex valued functions b can be inferred.