Absence of eigenvalues of Dirac and Pauli Hamiltonians via the method of multipliers

Abstract

By developing the method of multipliers, we establish sufficient conditions on the magnetic field and the complex, matrix-valued electric potential, which guarantee that the corresponding system of Schrödinger operators has no point spectrum. In particular, this allows us to prove analogous results for Pauli operators under the same electromagnetic conditions and, in turn, as a consequence of the supersymmetric structure, also for magnetic Dirac operators.

arXiv comment43 pages

References in corpus (6)

• Carleman estimates and absence of embedded eigenvalues
• Eigenvalue estimates for non-selfadjoint Dirac operators on the real line
• Eigenvalues of one-dimensional non-self-adjoint Dirac operators and applications
• Limiting absorption principle and Strichartz estimates for Dirac operators in two and higher dimensions
• Location of eigenvalues of three-dimensional non-self-adjoint Dirac operators
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Cited by in corpus (8)

• Eigenvalue bounds for non-selfadjoint Dirac operators
• Localization of eigenvalues for non-self-adjoint Dirac and Klein-Gordon operators
• Keller-type bounds for Dirac operators perturbed by rigid potentials
• Pseudomodes for non-self-adjoint Dirac operators
• Asymptotics for eigenvalues of one-dimensional Dirac operators in the weak coupling limit
• Decay of solutions of nonlinear Dirac equations
• The virial theorem and the method of multipliers in spectral theory
• From Lieb-Thirring inequalities to spectral enclosures for the damped wave equation