2021/08/31 by P. A. Nosov, Ivan M. Khaymovich, I. M. Khaymovich +2
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Born approximation #Eigenvalues and eigenvectors #Function (biology) #Green's function #Mathematical analysis #Mathematics #Matrix (chemical analysis) #Physics #Quantum many-body systems #Quantum mechanics #Scattering #Tree (set theory) #cond-mat.dis-nn #math-ph #math.MP #quant-ph
paper · pdf · doi:10.21468/scipostphys.12.2.048
published as SciPost Phys. 12, 048 (2022) · 24 pages, 4 figures, 39 references
arxiv created 2021/11/03 · openalex publication_date 2022/02/01 · arxiv updated 2022/02/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The accuracy of the forward scattering approximation for two-point Green's functions of the Anderson localization model on the Cayley tree is studied. A relationship between the moments of the Green's function and the largest eigenvalue of the linearized transfer-matrix equation is proved in the framework of the supersymmetric functional-integral method. The new large-disorder approximation for this eigenvalue is derived and its accuracy is established. Using this approximation the probability distribution of the two-point Green's function is found and compared with that in the forward scattering approximation (FSA). It is shown that FSA overestimates the role of resonances and thus the probability for the Green's function to be significantly larger than its typical value. The error of FSA increases with increasing the distance between points in a two-point Green's function.