Local Wegner and Lifshitz tails estimates for the density of states for continuous random Schrödinger operators

We introduce and prove local Wegner estimates for continuous generalized Anderson Hamiltonians, where the single-site random variables are independent but not necessarily identically distributed. In particular, we get Wegner estimates with a constant that goes to zero as we approach the bottom of th...

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Veröffentlicht in:	Journal of mathematical physics 2014-08, Vol.55 (8), p.1
Hauptverfasser:	Combes, Jean-Michel, Germinet, François, Klein, Abel
Format:	Artikel
Sprache:	eng
Schlagworte:	Density Density of states Estimates Independent variables Mathematical Physics Operators (mathematics) Physics Quantum physics Random variables Schrodinger equation Upper bounds
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container_title	Journal of mathematical physics
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creator	Combes, Jean-Michel Germinet, François Klein, Abel
description	We introduce and prove local Wegner estimates for continuous generalized Anderson Hamiltonians, where the single-site random variables are independent but not necessarily identically distributed. In particular, we get Wegner estimates with a constant that goes to zero as we approach the bottom of the spectrum. As an application, we show that the (differentiated) density of states exhibits the same Lifshitz tails upper bound as the integrated density of states.
doi_str_mv	10.1063/1.4893337
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subjects	Density Density of states Estimates Independent variables Mathematical Physics Operators (mathematics) Physics Quantum physics Random variables Schrodinger equation Upper bounds
title	Local Wegner and Lifshitz tails estimates for the density of states for continuous random Schrödinger operators
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