All ETDs from UAB

Advisory Committee Chair

Gunter Stolz

Advisory Committee Members

Christian Hainzl

Ryoichi Kawai

Boris Kunin

Zhijian Wu

Document Type


Date of Award


Degree Name by School

Doctor of Philosophy (PhD) College of Arts and Sciences


Central to the study of the motion of an electron in a structurally disordered medium under a tight-binding approximation is the family of discrete Schrodinger operators of the form h +V. The h term models the kinetic energy of the electron and the potential term V models the medium, the environment through which the electron moves. The potential V, indexed by a so-called displacement configuration, is formed by summing identical single-site potentials which have been displaced from the points of a sublattice of Z. The goal of this work is to investigate certain spectral properties of the operators h + V. More specifically, we investigate which displacement configurations give the smallest (and largest) almost-sure spectral minimum (and maximum). We address uniqueness questions and give a detailed discussion of the simplest one-dimensional case, the Bernoulli displacement model.



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