Ballistic electron motion in a random magnetic field

作者：K. B. Efetov, V. R. Kogan · 发表于：Physical review. B, Condensed matter · 年份：2003 · DOI：10.1103/physrevb.68.245313 · 被引用次数：4 · 研究领域：Quantum and electron transport phenomena、Quantum chaos and dynamical systems、Plasma Diagnostics and Applications

Using a scheme of the derivation of the nonlinear $\ensuremath{\sigma}$ 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 ${Q}^{2}=1.$ Contrary to the standard scheme, neither singling out slow modes nor saddle-point approximations are used. The $\ensuremath{\sigma}$ 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 $\ensuremath{\sigma}$ model is obtained leading to the conventional localization behavior.