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arXiv · 2204.13947

Limiting distribution of extremal eigenvalues of d-dimensional random Schr\"odinger operator

Kaito Kawaai·Yugo Maruyama·Fumihiko Nakano
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Abstract

We consider Schr\"odinger operator with random decaying potential on $\ell^2 ({\bf Z}^d)$ and showed that, (i) IDS coincides with that of free Laplacian in general cases, and (ii) the set of extremal eigenvalues, after rescaling, converges to a inhomogeneous Poisson process, under certain condition on the single-site distribution, and (iii) there are "border-line" cases, such that we have Poisson statistics in the sense of (ii) above if the potential does not decay, while we do not if the potential does decay.

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Kaito Kawaai, Yugo Maruyama, Fumihiko Nakano. 2022-04-29. Limiting distribution of extremal eigenvalues of d-dimensional random Schr\"odinger operator. https://doi.org/10.1142/s0129055x22500416

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