Absolutely continuous and pure point spectra of discrete operators with sparse potentials
We consider the discrete Schrödinger operator $H=-Δ+V$ with a sparse potential $V$ and find conditions guaranteeing either existence of wave operators for the pair $H$ and $H_0=-Δ$, or presence of dense purely point spectrum of the operator $H$ on some interval $[λ_0,0]$ with $λ_0<0$.
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