Eigenvalue statistics for Schrödinger operators with random point interactions on ℝ^d, d=1,2,3

2019/05/20 by Hislop, Peter D., Kirsch, Werner, Krishna, M. · 2 citations
#35J10 #35P20 #81Q10 #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1905.07889

Abstract

We prove that the local eigenvalue statistics at energy E in the localization regime for Schrödinger operators with random point interactions on ℝ^d, for d=1,2,3, is a Poisson point process with the intensity measure given by the density of states at E times the Lebesgue measure. This is one of the first examples of Poisson eigenvalue statistics for the localization regime of multi-dimensional random Schrödinger operators in the continuum. The special structure of resolvent of Schrödinger operators with point interactions facilitates the proof of the Minami estimate for these models.

Cited by

• Dynamical localization and delocalization for random Schrodinger operators with δ-interactions in ℝ³
• Real-Analyticity of the Density of States for Random Schrödinger operators with Point Interactions

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