The landscape law for the integrated density of states

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

paper · doi:10.48550/arxiv.1909.10558

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
• Landscape estimates of the integrated density of states for Jacobi operators on graphs
• The Integrated Density of States for Random Schroedinger Operators
• Regularity of the Surface Density of States