Localization of Eigenstates and Transport Phenomena in the One-Dimensional Disordered System

Abstract

Some exact results obtained by now are reviewed. A most general proof is given for the exponential growth of particular solutions. Based on this property a unification is brought about into the theories on localization of eigenstates, transmission problem, heat conduction through harmonic chains, and quantum diffusion problem. Singular properties are proved for the Green function and the spectrum of the disordered system. Vanishing of the d.c. conductivity is discussed and numerically calculated eigenstates are collected.