Fluctuation spectrum of the electron states in a two-dimensional system with a Gaussian potential and a transverse magnetic field

The results of the investigation of the fluctuation region of the electron spectrum in a two-dimensional system with a Gaussian white-noise potential and a perpendicular magnetic field are presented. We use the optimal fluctuation method and calculate both the density of states and the localization length in the whole fluctuation region below the lowest Landau level. We describe all possible structures of the quantum fluctuation region and establish limits on the applicability of the white-noise-potential model as well as on the approximation based upon the projection onto the lowest Landau level.