# Eigenvalues of one-dimensional non-self-adjoint Dirac operators and applications

## TL;DR

This paper studies the eigenvalues of one-dimensional non-self-adjoint Dirac operators with complex potentials, providing new asymptotic results, inequalities, and applications to physics such as wave damping and graphene nanoribbons.

## Contribution

It introduces new analysis of eigenvalues for non-self-adjoint Dirac operators, including existence, asymptotics, and inequalities, with applications to physical models.

## Key findings

- Existence and asymptotics of weakly coupled eigenvalues
- Lieb-Thirring inequalities for non-self-adjoint operators
- Applications to damped wave equations and graphene nanoribbons

## Abstract

We analyze eigenvalues emerging from thresholds of the essential spectrum of one-dimensional Dirac operators perturbed by complex and non-symmetric potentials. In the general non-self-adjoint setting we establish the existence and asymptotics of weakly coupled eigenvalues and Lieb-Thirring inequalities. As physical applications we investigate the damped wave equation and armchair graphene nanoribbons.