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Eigenvalue statistics for Schrödinger operators with random point interactions on R d, d = 1, 2, 3
P.D. Hislop, W. Kirsch,
Published in American Institute of Physics Inc.
2020
Volume: 61
   
Issue: 9
Abstract
We prove that the local eigenvalue statistics at energy E in the localization regime for Schrödinger operators with random point interactions on Rd, 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. © 2020 Author(s).
About the journal
JournalData powered by TypesetJournal of Mathematical Physics
PublisherData powered by TypesetAmerican Institute of Physics Inc.
ISSN00222488