Eigenvalue statistics for Schrödinger operators with random point interactions on $\mathbb{R}^d$, $d=1,2,3$
We prove that the local eigenvalue statistics at energy $E$ in the localization regime for Schr\"odinger operators with random point interactions on $\mathbb{R}^d$, 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 Schr\"odinger operators in the continuum. The special structure of resolvent of Schr\"odinger operators with point interactions facilitates the proof of the Minami estimate for these models.
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Peter D. Hislop (edit)
Werner Kirsch (add twitter)
M. Krishna (edit)
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05/20/19 06:05PM
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MathPHYPapers: Eigenvalue statistics for Schr\"odinger operators with random point interactions on $\mathbb{R}^d$, $d=1,2,3$. https://t.co/VCA3HVvwC7
mathMPb: Peter D. Hislop, Werner Kirsch, M. Krishna : Eigenvalue statistics for Schrödinger operators with random point interactions on $\mathbb{R}^d$, $d=1,2,3$ https://t.co/9Ou4PCj15M https://t.co/lmlBiWd1zK
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