Statistics of Green's functions on a disordered Cayley tree and the validity of forward scattering approximation

Journal Article · 01 February 2022 · SciPost Physics

DOI: https://doi.org/10.21468/SciPostPhys.12.2.048 · OSTI ID:1843051

Nosov, Pavel ^[1]; Khaymovich, Ivan ^[2]; Kudlis, Andrey ^[3]; Kravtsov, Vladimir ^[4]

---

1. Stanford University
2. Max Planck Institute for the Physics of Complex Systems, Institute for Physics of Microstructures, Russian Academy of Sciences
3. ITMO University
4. Abdus Salam International Centre for Theoretical Physics, Landau Institute for Theoretical Physics

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.

• Sponsoring Organization: USDOE
• Grant/Contract Number: AC02-76SF00515
• OSTI ID: 1843051
• Journal Information: SciPost Physics, Journal Name: SciPost Physics Journal Issue: 2 Vol. 12; ISSN 2542-4653
• Publisher: Stichting SciPostCopyright Statement
• Country of Publication: Netherlands
• Language: English