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

Jean-Claude Cuenin; Petr Siegl

doi:10.1007/s11005-018-1051-6

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

Jean-Claude Cuenin, Petr Siegl

School of Mathematics and Physics

Research output: Contribution to journal › Article › peer-review

9 Citations (Scopus)

150 Downloads (Pure)

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.

Original language	English
Journal	Letters in Mathematical Physics
Early online date	31 Jan 2018
DOIs	https://doi.org/10.1007/s11005-018-1051-6
Publication status	Early online date - 31 Jan 2018

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

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AB - 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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