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

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.