Transmission resonances and the localization length in one-dimensional disordered systems

Abstract

Numerically obtained results concerning the transmittance and localization length of a one-dimensional disordered system are presented. We show that as a function of the energy of the incoming particle the transmittance is characterized by randomly positioned exponentially narrow resonances. Depending upon the relationship between the length of the system and the localization length, the transmittance may appear to be either a perfectly smooth function of energy (the resonances being invisible on any practical energy scale) or a highly structured function varying in a random way.