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Full distribution of the ground-state energy of potentials with weak disorder

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We study the full distribution P(E) of the ground-state energy of a single quantum particle in a potential V(x)=V_{0}(x)+sqrt[ε]v_{1}(x), where V_{0}(x) is a deterministic "background" trapping potential and v_{1}(x) is the disorder. We consider arbitrary t... ...