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

2021/08/08 by Wenwen Jian, Yingte Sun, Wenwen, Jian +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical methods in inverse problems #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2108.03589

openalex publication_date 2021/08/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we prove a power-law version dynamical localization for a random operator H_ω on ℤ^d with long-range hopping. In breif, for the linear Schrödinger equation i∂_tu=H_ωu, u ∈ ℓ²(ℤ^d), the Sobolev norm of the solution with well localized initial state is bounded for any t≥ 0.

Citations

• Anderson localization for Bernoulli and other singular potentials

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