Extended states in a one-demensional system with off-diagonal disorder

We prove for a one-dimensional tight-binding Hamiltonian with only off-diagonal randomness that the state at the middle of the band is extended, regardless of the probability distribution of the hopping matrix elements and also derive a sum rule for the density of states. In particular, for the case where the probability distribution of the hopping matrix elements is a generalized Poisson distribution, we derive an expression for the localization length near the middle of the band. We also calculate the localization length for a chain of potential wells with randomly fluctuating depths, separated by regions of zero potential, the length of the latter being also random.