On the Spectrum of a Discrete Non-Hermitian Quantum System

TL;DR

This paper analyzes the spectral properties of a discrete non-Hermitian quantum system, establishing conditions for when its spectrum is discrete, thus contributing to understanding non-Hermitian quantum models on complex contours.

Contribution

It introduces spectral analysis methods for a discrete non-Hermitian quantum system and provides simple criteria for the discreteness of its spectrum.

Findings

Established conditions for the spectrum to be discrete.

Developed spectral analysis techniques for non-Hermitian systems.

Linked discrete models to continuous quantum systems on complex contours.

Abstract

In this paper, we develop spectral analysis of a discrete non-Hermitian quantum system that is a discrete counterpart of some continuous quantum systems on a complex contour. In particular, simple conditions for discreteness of the spectrum are established.