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Well-posedness and instability of free electron quantum tomography
Florian Oberender
Recent advancements in photon induced near-field electron microscopy (PINEM) enable the preparation, coherent manipulation and characterization of free-electron quantum states. The…
Quantum relative entropy regularization for quantum state tomography
Florian Oberender, Thorsten Hohage
The density matrix is a positive semidefinite operator of trace 1 characterizing the state of a quantum system. We consider the inverse problem to reconstruct such density matrices…
On the instabilities of naive FEM discretizations for PDEs with sign-changing coefficients
Martin Halla, Florian Oberender
We consider a scalar diffusion equation with a sign-changing coefficient in its principle part. The well-posedness of such problems has already been studied extensively provided th…
A new numerical method for scalar eigenvalue problems in heterogeneous, dispersive, sign-changing materials
Martin Halla, Thorsten Hohage, Florian Oberender
We consider time-harmonic scalar transmission problems between dielectric and dispersive materials with generalized Lorentz frequency laws. For certain frequency ranges such equati…