Optimal dispersion for discrete periodic Schrödinger operators

2025/05/20 by David Damanik, Jake Fillman, Damanik, David +3 · 2 citations
Engineering · Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Microwave Imaging and Scattering Analysis #Numerical methods in inverse problems #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2505.14475

openalex publication_date 2025/05/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove a dispersive estimate for periodic discrete Schrödinger operators on the line with optimal rate of decay. Additionally, by standard methods, we deduce dispersive estimates for the discrete nonlinear Schrödinger equation with small initial data and suitable nonlinearity when the underlying Hamiltonian is periodic.

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