Spectrum for a non-unitary one-dimensional two-state quantum walk with one defect

TL;DR

This paper investigates the eigenvalues of a non-unitary, one-dimensional two-state quantum walk with a defect, revealing insights into localization and topological properties in non-Hermitian quantum systems.

Contribution

It provides a comprehensive analysis of eigenvalues for non-unitary quantum walks with chiral symmetry and a defect, advancing understanding of their spectral properties.

Findings

Eigenvalues are characterized for the non-unitary quantum walk with a defect.

The study links eigenvalues to localization phenomena.

Insights into topological features of non-Hermitian quantum systems.

Abstract

Existence of the eigenvalues of the discrete-time quantum walks is deeply related to localization. Also, for the study of open quantum systems, non-Hermitian systems have attracted much attention. As mathematical models for such systems, non-unitary quantum walks with the chiral symmetry are essential for the study of the topological insulator. In this paper, we give the whole picture of the eigenvalues of a non-unitary one-dimensional two-state quantum walks with one defect and the chiral symmetry.