Localization of Quantum Electrons in One, Two and Three Dimensional Disordered Systems of Scatterers. Monte Carlo Investigations

Path integrals and complex Monte Carlo method are formulated for the system of noninteracting electrons in a random potential of scatterers and external electrical field. The ensemble-averaged probability for electron with energy E to travel a distance \( \left| {r - r'} \right| \) have been calculated. The numerical results for 1D, 2D and 3D disordered systems have been obtained and compared with analytical results. The unwaited sharp peaks, which interrupt the exponential decay of the mean squared value of the Green function modulus and delocalization of electrons in external electrical field have been also obtained.