2023/02/01 by Arka Adhikari, Adhikari, Arka, Sofiia Dubova +5 · 2 citations
Biochemistry, Genetics and Molecular Biology · Chemistry · Physics and Astronomy · #Electron Spin Resonance Studies #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Molecular spectroscopy and chirality #Probability (math.PR) #Quantum optics and atomic interactions
paper · pdf · doi:10.48550/arxiv.2302.00157
openalex publication_date 2023/02/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we extend results of Eigenvector Thermalization to the case of generalized Wigner matrices. Analytically, the central quantity of interest here are multiresolvent traces, such as ΛA:= (1)/(N) Tr GAGA. In the case of Wigner matrices, as in \citecipolloni-erdos-schroder-2021, one can form a self-consistent equation for a single ΛA. There are multiple difficulties extending this logic to the case of general covariances. The correlation structure prevents us from deriving a self-consistent equation for a single matrix A; this is due to the introduction of new terms that are quite distinct from the form of ΛA. We find a way around this by carefully splitting these new terms and writing them as sums of ΛB, for matrices B obtained by modifying A using the covariance matrix. The result is a system of self-consistent equations relating families of deterministic matrices. Our main effort in this work is to derive and analyze this system of self-consistent equations.