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Duality methods in networks, computer science models, and disordered condensed matter systems

dc.contributor.advisorGalitski, Victor Men_US
dc.contributor.authorMitchell, Joe Danen_US
dc.description.abstractIn this thesis, I explore lattice independent duality and systems to which it can be applied. I first demonstrate classical duality on models in an external field, including the Ising, Potts, and x-y models, showing in particular how this modifies duality to be lattice independent and applicable to networks. I then present a novel application of duality on the boolean satsifiability problem, one of the most important problems in computational complexity, through mapping to a low temperature Ising model. This establishes the equivalence between boolean satisfiability and a problem of enumerating the positive solutions to a Diophantine system of equations. I continue by combining duality with a prominent tool for models on networks, belief propagation, deriving a new message passing procedure, dual belief propagation. In the final part of my thesis, I shift to propose and examine a semiclassical model, the two-component Coulomb glass model, which can explain the giant magnetoresistance peak present in disordered films near a superconductor-insulator transition as the effect of competition between single particle and localized pair transport. I numerically analyze the density of states and transport properties of this model.en_US
dc.titleDuality methods in networks, computer science models, and disordered condensed matter systemsen_US
dc.contributor.publisherDigital Repository at the University of Marylanden_US
dc.contributor.publisherUniversity of Maryland (College Park, Md.)en_US
dc.subject.pqcontrolledCondensed matter physicsen_US
dc.subject.pqcontrolledComputer scienceen_US
dc.subject.pquncontrolledcoulomb glassen_US
dc.subject.pquncontrolledkramers wannieren_US

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