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

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.

16 pages

References in corpus (2)

• Self-adjointness of two-dimensional Dirac operators on domains
• Dipoles in Graphene Have Infinitely Many Bound States

Cited by in corpus (11)

• Absence of eigenvalues of Dirac and Pauli Hamiltonians via the method of multipliers
• Location of eigenvalues of non-self-adjoint discrete Dirac operators
• Location of eigenvalues of three-dimensional non-self-adjoint Dirac operators
• Eigenvalue bounds for non-selfadjoint Dirac operators
• Eigenvalue estimates for bilayer graphene
• Keller-type bounds for Dirac operators perturbed by rigid potentials
• Pseudomodes for non-self-adjoint Dirac operators
• Dirac fermions in armchair graphene nanoribbons trapped by electric quantum dots
• From Lieb-Thirring inequalities to spectral enclosures for the damped wave equation
• The relativistic rotated harmonic oscillator
• Asymptotics for eigenvalues of one-dimensional Dirac operators in the weak coupling limit