1D Disordered System with Periodic Boundary Conditions : Density of States and Shape of Wavefunctions

Abstract

By example of a one-dimensional relativistic random electron problem, we show that the states of ld disordered systems are strongly influenced by the kind of boundary conditions imposed. Treating the spatial propagation of the wavefunctions within the framework of the transfer matrix method, we find that periodic boundary conditions only become possible if we do not fix the value of the wavefunctions at the edges of the system : Periodic boundary conditions induce a certain kind of correlation between the “random sequence” characterizing the disordered system and the space dependence of the wavefunctions. Since this correlation is absent for fixed boundary conditions we are led to an argument making the “localisation of almost all states” in the usual sense highly unplausible for periodic boundary conditions.