The landscape law for the integrated density of states

2019/09/23 by Guy David, David, Guy, Marcel Filoche +3 · 3 citations
Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.AP #math.MP

paper · pdf · doi:10.48550/arxiv.1909.10558

arxiv created 2021/06/05 · arxiv updated 2021/06/08

Abstract

The present paper establishes non-asymptotic estimates from above and below on the integrated density of states of the Schrödinger operator L=-Δ+V, using a counting function for the minima of the localization landscape, a solution to the equation Lu=1.

Cited by

• Localization-landscape generalized Mott-Berezinskiĭ formula
• Testing the Localization Landscape Theory on the Bethe Lattice
• Localization structure of electronic states in the quantum Hall effect

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• Localization of Quantum States and Landscape Functions
• The density of states depends on the domain
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• The Integrated Density of States for Random Schroedinger Operators
• Regularity of the Surface Density of States