Orthogonal polynomials induced by discrete-time quantum walks in one dimension

TL;DR

This paper explores the properties of orthogonal polynomials derived from the limit density of a rescaled one-dimensional discrete-time quantum walk, revealing new mathematical structures related to quantum walk dynamics.

Contribution

It introduces a novel class of orthogonal polynomials associated with quantum walks and analyzes their properties, connecting quantum walk limit densities with orthogonal polynomial theory.

Findings

Identification of orthogonal polynomials linked to quantum walk limit densities

Analysis of polynomial properties derived from quantum walk dynamics

Establishment of connections between quantum walks and classical orthogonal polynomial theory

Abstract

In this paper we obtain some properties of orthogonal polynomials given by a weight function which is a limit density of a rescaled discrete-time quantum walk on the line.