On Dispersive Decay for Discrete 3D Schr\"odinger and Klein-Gordon Equations

TL;DR

This paper establishes the long-time decay rates in weighted norms for solutions to the discrete three-dimensional Schr"odinger and Klein-Gordon equations, enhancing understanding of their dispersive properties.

Contribution

It provides new decay estimates for these equations, which were previously not well-understood in the discrete 3D setting.

Findings

Derived decay rates for discrete 3D Schr"odinger solutions

Established decay estimates for discrete 3D Klein-Gordon solutions

Enhanced understanding of dispersive behavior in discrete quantum models

Abstract

We derive the long-time decay in weighted norms for solutions of the discrete 3D Schr\"odinger and Klein-Gordon equations.