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Cuenin, Jean-Claude and Siegl, Petr (2018): Eigenvalues of one-dimensional non-self-adjoint Dirac operators and applications. In: Letters in Mathematical Physics, Vol. 108, No. 7: pp. 1757-1778

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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.

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