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Density of states and level statistics for 1d Schroedinger operators Nakano, Fumihiko

Description

We consider the 1d Schroedinger operator with random potential decaying of order \(\alpha\). The results are : (1) the fluctuation of density of states with different behavior depending on \(\alpha\), (2) the level statistics asymptotically obeys clock, \(Sine_{\beta}\), and Poisson processes for super-critical, critical, and sub-critical cases, respectively.

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