8 papers · 1 filter
Abrupt changes in the spectra of the Laplacian with constant complex magnetic field
David Krejcirik, Tho Nguyen Duc, Nicolas Raymond
We analyze the spectrum of the Laplace operator, subject to homogeneous complex magnetic fields in the plane. For real magnetic fields, it is well-known that the spectrum consists…
The relativistic rotated harmonic oscillator
A. Balmaseda, D. Krejcirik, J. M. Pérez-Pardo
We introduce a relativistic version of the non-self-adjoint operator obtained by a dilation analytic transformation of the quantum harmonic oscillator. While the spectrum is real a…
The Laplacian with complex magnetic fields
David Krejcirik, Tho Nguyen Duc, Nicolas Raymond
We study the two-dimensional magnetic Laplacian when the magnetic field is allowed to be complex-valued. Under the assumption that the imaginary part of the magnetic potential is r…
A note on the failure of the Faber-Krahn inequality for the vector Laplacian
David Krejcirik, Pier Domenico Lamberti, Michele Zaccaron
We consider a natural eigenvalue problem for the vector Laplacian related to stationary Maxwell's equations in a cavity and we prove that an analog of the celebrated Faber-Krahn in…
Spectral analysis of Dirac operators for dislocated potentials with a purely imaginary jump
Lyonell Boulton, David Krejcirik, Tho Nguyen Duc
In this paper we present a complete spectral analysis of Dirac operators with non-Hermitian matrix potentials of the form where . For …
The virial theorem and the method of multipliers in spectral theory
Lucrezia Cossetti, David Krejcirik
We provide a link between the virial theorem in functional analysis and the method of multipliers in theory of partial differential equations. After giving a physical insight into…
Dirac operators on the half-line: stability of spectrum and non-relativistic limit
David Kramar, David Krejcirik
We consider Dirac operators on the half-line, subject to generalised infinite-mass boundary conditions. We derive sufficient conditions which guarantee the stability of the spectru…
Spectral determinant for the wave equation on an interval with Dirac damping
David Krejcirik, Jiri Lipovsky
A closed formula for the spectral determinant for the wave equation on a bounded interval, subject to Dirichlet boundary conditions and an -multiple of the Dirac -type dampin…