Dynamical localization for polynomial long-range hopping random operators on ℤ^{𝕕}

Jian, Wenwen; Sun, Yingte

doi:10.1090/proc/16094

Dynamical localization for polynomial long-range hopping random operators on $\mathbb {Z}^d$
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by Wenwen Jian and Yingte Sun PDF

Proc. Amer. Math. Soc. 150 (2022), 5369-5381 Request permission

Abstract:

In this paper, we prove a power-law version dynamical localization for a random operator $\mathrm {H}_{\omega }$ on $\mathbb {Z}^d$ with long-range hopping. In brief, we show that the Sobolev norm of the discrete linear Schrödinger equation $\mathrm {i}\partial _{t}u=\mathrm {H}_{\omega }u$ with well-localized initial state is bounded for any $t\geq 0$.

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