LOCALIZATION IN A STRONGLY DISORDERED SYSTEM: A PERTURBATION APPROACH

2006/04/30 by Marco Frasca
Physics and Astronomy · #Quantum and electron transport phenomena #Quantum chaos and dynamical systems #Theoretical and Computational Physics #cond-mat.dis-nn #hep-th #quant-ph

paper · pdf · doi:10.1142/s0217979213500513

published as Int.J.Mod.Phys.B27:1350051,2013 · 5 pages, no figures. Version accepted for publication on International Journal of Modern Physics B

arxiv created 2008/10/10 · openalex publication_date 2013/05/02 · arxiv updated 2013/05/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We prove that a strongly disordered two-dimensional system localizes with a localization length given analytically. We get a scaling law with a critical exponent ν = 1 in agreement with the Chayes criterion ν ≥ 1. The case we are considering is for off-diagonal disorder. The method we use is a perturbation approach holding in the limit of an infinitely large perturbation as recently devised and the Anderson model is considered with a Gaussian distribution of disorder. The localization length diverges when energy goes to zero with a scaling law in agreement to numerical and theoretical expectations.

Citations

• Cooperative effects in Josephson junctions in a cavity in the strong coupling regime
• Metal–insulator transition in two-dimensional electron systems
• Metal-Insulator Transition in Disordered Two-Dimensional Electron Systems
• Third-order correction to localization in a two-level driven system
• Exponents of the localization length in the 2D Anderson model with off‐diagonal disorder
• Scaling Theory of Localization: Absence of Quantum Diffusion in Two Dimensions