Eigenvalue bounds for Stark operators with complex potentials
Evgeny Korotyaev, Oleg Safronov
TL;DR
This paper investigates the spectral properties of a 3D Stark operator with a complex potential, providing bounds on the number and sum of eigenvalues in the upper half-plane, advancing understanding of non-self-adjoint operators.
Contribution
It introduces new eigenvalue bounds for the Stark operator with complex potentials, extending spectral analysis techniques to non-self-adjoint cases.
Findings
Derived estimates for the number of eigenvalues.
Established bounds on the sum of imaginary parts of eigenvalues.
Enhanced understanding of spectral behavior of complex Stark operators.
Abstract
We consider the 3-dimensional Stark operator perturbed by a complex-valued potential. We obtain an estimate for the number of eigenvalues of this operator as well as for the sum of imaginary parts of eigenvalues situated in the upper half-plane.
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