2003/07/31 by K. B. Efetov, V. R. Kogan
Engineering · Physics and Astronomy · #Plasma Diagnostics and Applications #Quantum and electron transport phenomena #Quantum chaos and dynamical systems #cond-mat.dis-nn #cond-mat.mes-hall
paper · pdf · doi:10.1103/physrevb.68.245313
published as Phys. Rev. B 68, 245313 (2003) · 10 pages, no figures, to be submitted in PRB v2: Section IV is removed
arxiv created 2003/10/14 · openalex publication_date 2003/12/18 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Using a scheme of the derivation of the nonlinear \ensuremathσ model we consider the electron motion in a random magnetic field in two dimensions. The derivation is based on writing quasiclassical equations and representing their solutions in terms of a functional integral over supermatrices Q with the constraint Q2=1. Contrary to the standard scheme, neither singling out slow modes nor saddle-point approximations are used. The \ensuremathσ model obtained is applicable at the length scale down to the electron wavelength. We show that this model differs from the model with a random potential. However, after averaging over fluctuations in the Lyapunov region the standard \ensuremathσ model is obtained leading to the conventional localization behavior.