Electron in saddle point and random potentials of quantum hall system

Abstract

An electron moving in two dimensions under the influence of a transverse magnetic field and an anisotropic saddle point potential Vsp(X,Y) = V0 + (m/2)(omega x square X square -omega y square y square) was proposed by Fertig and Halperin for studying the tunneling and delocalization of electrons in the quantum Hall problem. The exact propagator for an electron in the isotropic case which omega x square = omega y square was considered by Kagalovsky by using the Feynman path integral, and the matrix method introduced by Papadopoulos. In this thesis, we derive the exact propagator for an electron in the anisotropic case by using the Feynman path integral. Our result is applied to calculate the density of states. It is shown that the energy of the Landau level of Fertig and Halperin can be obtained from the path integral and the delocalization of electrons is discussed. For the isotropic anharmonic oscillator we obtain the result of Kagalovsky.