Electrical resistance of disordered one-dimensional lattices

Abstract

The electrical resistance of a Fermi gas in a completely disordered one-dimensional lattice is evaluated. The wavefunctions of the electrically unperturbed lattice are used to evaluate a diffusion coefficient, and the Einstein relation then leads to the resistance. An ensemble averaging process is invoked, in which the distances between adjacent obstacles are varied independently of one another with an equal probability for all possible phase relationships between adjacent obstacles. The result is a resistance growing exponentially, rather than linearly with the number of obstaoles. This is believed to be related to earlier results by others observing localizing wave-functions due to the prevalence of exponentially decaying wavefunctions. © 1970 Taylor & Francis Group, LLC.