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Mean Value Sets and Kakutani-Feynman-Kac formulas for Differential Operators with Rough Coefficients

Martini, James

Description

Eigenfunctions of Schrodinger operators L := −divA∇ + V are observed to localise to a number of coupled subregions of the domain U ⊂ Rd when the coefficients A, potential V are irregular, or when the domain has a complicated geometry. These situations provide a mathematical model for the Anderson localisation phenomenon in physics, which is the observation that particles in disordered materials will diffuse very slowly or effectively not at all outside of specific subregions. Filoche, Mayboroda...[Show more]

CollectionsOpen Access Theses
Date published: 2023
Type: Thesis (MPhil)
URI: http://hdl.handle.net/1885/299728
DOI: 10.25911/XJHR-VQ40

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