New class of exactly solvable one-dimensional disordered electron hopping systems

Two types of disordered chains are presented, which allow for the exact calculation of the (configurational averaged) density of states in terms of a continued fraction. The first model contains a certain type of site-diagonal disorder and is a generalization of Lloyd's model; it refers to a substitutional alloy.The second model contains site-off-diagonal (hopping) disorder and may refer to a generalized alloy—analog treatment of a Hubbard chain.