Occupation time for classical and quantum walks

TL;DR

This paper explores the concept of occupation time in classical and quantum walks, aiming to shed light on their behaviors and differences through illustrative figures, serving as an invitation to further study in this emerging area.

Contribution

It introduces and visualizes occupation time phenomena in classical and quantum walks, highlighting unexplored aspects and encouraging further research.

Findings

Illustrative figures demonstrate occupation time behaviors

Highlights differences between classical and quantum walks

Encourages further theoretical and experimental investigation

Abstract

This is a personal tribute to Lance Littlejohn on the occasion of his 70th birthday. It is meant as a present to him for many years of friendship. It is not written in the "Satz-Beweis" style of Edmund Landau or even in the format of a standard mathematics paper. It is rather an invitation to a fairly new, largely unexplored, topic in the hope that Lance will read it some afternoon and enjoy it. If he cares about complete proofs he will have to wait a bit longer; we almost have them but not in time for this volume. We hope that the figures will convince him and other readers that the phenomena displayed here are interesting enough.