Exact two-dimensional propagator of an electron in magnetic and electric fields with a quadratic random potential

Abstract

The exact two-dimensional propagator of an electron moving in a transverse magnetic field and a time-varying electric field with a one-parameter nonlocal harmonic random potential was calculated exactly using the Feynman path integral method by considering the Stratonovich's transformation and the 2x2 matrices methods. In this thesis, we introduce the nonlocal harmonic random potential with two parameters. The exact two-dimensional propagator in a transverse magnetic field and an electric field with a two-parameter nonlocal harmonic potential cannot be calculated exactly. However, we can evaluate the analytic propagator by separating the Lagrangian into two parts. The first part can be calculated exactly by the two-particle model method. The second part can be calculated by first-order cumulant approximation. The density of states with a Gaussian random potential can be calculated by the variational path integral method in the low and high energy limits, respectively. In addition, we compare the density of states with the one-parameter theory and the tight-binding simulation result in the white noise limit