A limit law of the return probability for a quantum walk on a hexagonal lattice

TL;DR

This paper investigates the long-term behavior of the return probability for a specific quantum walk model on a hexagonal lattice, revealing how quantum dynamics are influenced by lattice structure.

Contribution

It establishes a limit law for the return probability of a 3-state discrete-time quantum walk on a hexagonal lattice, advancing understanding of quantum walk behavior on complex structures.

Findings

Derived a limit law for the return probability

Showed dependence of return probability on lattice structure

Enhanced understanding of quantum walk dynamics

Abstract

A return probability of random walks is one of the interesting subjects. As it is well known, the return probability strongly depends on the structure of the space where the random waker moves. On the other hand, the return probability of quantum walks, which are quantum models corresponding to random walks, has also been investigated to some extend lately. In this paper, we present a limit of the return probability for a discrete-time 3-state quantum walk on a hexagonal lattice.