Periodic boundary conditions for a 1d disordered system: Influence on the density of states and the shape of the wavefunctions

For a special one-dimensional disordered system which allows a particularly transparent investigation of the kind of problem in question, we study how the density of states and the detailed shape of the wavefunctions are influenced by changing the boundary conditions imposed on the system.The spatial propagation of the wavefunctions is treated within the framework of the transfer matrix method. Periodic boundary conditions only become possible if we do not fix the value of the wavefunctions at the edges of the system. They induce a certain correlation between the random sequence characterizing the disordered system and the space dependence of the wavefunctions. The existence of this kind of correlation then leads to an argument which, although not rigorous, makes localization of almost all states in the usual sense highly unplausible for periodic boundary conditions.