A remark on uniform Strichartz estimate for quantum walks on 1D lattice

TL;DR

This paper establishes uniform Strichartz estimates for quantum walks on a one-dimensional lattice, independent of the lattice spacing, advancing the mathematical understanding of quantum dynamics on discrete structures.

Contribution

It proves Strichartz estimates for quantum walks on 1D lattices that are uniform with respect to the lattice width, extending previous results to a discrete setting.

Findings

Strichartz estimates hold uniformly for quantum walks on 1D lattices.

The estimates are independent of the lattice spacing elta.

This work generalizes continuous quantum walk results to discrete lattices.

Abstract

In this short note, we study quantum walks (QWs) on one dimensional lattice $\delta \mathbb{Z}$. Following Hong-Yang, we prove Strichartz estimates for QWs independent of the lattice width $\delta$.