Supersymmetric Cluster Expansions and Applications to Random Schrödinger Operators
Keyword(s):
AbstractWe study discrete random Schrödinger operators via the supersymmetric formalism. We develop a cluster expansion that converges at both strong and weak disorder. We prove the exponential decay of the disorder-averaged Green’s function and the smoothness of the local density of states either at weak disorder and at energies in proximity of the unperturbed spectrum or at strong disorder and at any energy. As an application, we establish Lifshitz-tail-type estimates for the local density of states and thus localization at weak disorder.
2020 ◽
Vol 378
(1)
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pp. 299-328
2003 ◽
pp. 15-24
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2019 ◽
Vol 27
(4)
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pp. 253-259
2018 ◽
Vol 2020
(17)
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pp. 5279-5341
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2007 ◽
Vol 253
(2)
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pp. 515-533
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2004 ◽
pp. 97-183
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