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We consider eigenvalues of the Pauli operator in $\mathbb R^3$ embedded in the continuous spectrum. In our main result we prove the absence of such eigenvalues above a threshold which depends on the asymptotic behavior of the magnetic and…
The spectral analysis of a non-Hermitian unbounded operator appearing in quantum physics is our main concern. The properties of such an operator are essentially different from those of Hermitian Hamiltonians, namely due to spectral…
Electron diffraction from nanogratings provides a platform for free-electron interferometry, yet controlled manipulation of electron spin in such geometries remains largely unexplored. In particular, the role of the self-generated magnetic…
Tensor-valued and matrix-valued measurements of different physical properties are increasingly available in material sciences and medical imaging applications. The eigenvalues and eigenvectors of such multivariate data provide novel and…
We investigate transient radiation processes in the non-linear superradiance (SR) regime of the Doppler broadened Maxwell-Bloch equations when the velocity distribution is of total bandwidth greatly exceeding that of the transient process…
The distortion from massive MIMO (multiple-input--multiple-output) base stations with nonlinear amplifiers is studied and its radiation pattern is derived. The distortion is analyzed both in-band and out-of-band. By using an orthogonal…
The largest eigenvalue of random tensors is an important feature of systems involving disorder, equivalent to the ground state energy of glassy systems or to the injective norm of quantum states. For symmetric Gaussian random tensors of…
The open problem of calculating the limiting spectrum (or its Shannon transform) of increasingly large random Hermitian finite-band matrices is described. In general, these matrices include a finite number of non-zero diagonals around their…
W-band ({\nu} ca. 94 GHz) electron paramagnetic resonance (EPR) spectroscopy was used for a single-crystal study of a star-shaped Fe3Cr single-molecule magnet (SMM) with crystallographically imposed trigonal symmetry. The high resolution…
This paper focuses on random projection operators when the subspace of projection is estimated. We derive non-asymptotic upper bounds on the error between the projection onto the estimated subspace and the projection onto the underlying…
Gaussian cosmic microwave background skies are fully specified by the power spectrum. The conventional method of characterizing non-Gaussian skies is to evaluate higher order moments, the n-point functions and their Fourier transforms. We…
Model-driven analysis of biophysical phenomena is gaining increased attention and utility for medical imaging applications. In magnetic resonance imaging (MRI), the availability of well-established models for describing the relations…
Using extensive Brownian dynamics computer simulations, the long-time self-diffusion coefficient is calculated for Gaussian-core particles as a function of the number density. Both spherical and rod-like particles interacting via Gaussian…
We calculate the magnetic SANS cross section of dilute ensembles of uniformly magnetized and randomly-oriented Stoner-Wohlfarth particles using the Landau-Lifshitz equation. The focus of our study is on the angular anisotropy of the…
This article is concerned with uniqueness and stability issues for the inverse spectral problem of recovering the magnetic field and the electric potential in a Riemannian manifold from some asymptotic knowledge of the boundary spectral…
In this contribution we analyze the spectral properties of some commonly used boundary integral operators in computational electromagnetics and of their discrete counterparts, highlighting peculiar features of their spectra. In particular,…
In mathematical physics, the gradient operator with nonconstant coefficients encompasses various models, including Fourier's law for heat propagation and Fick's first law, that relates the diffusive flux to the gradient of the…
Despite the tremendous progresses in wavefront control through or inside complex scattering media, several limitations prevent reaching practical feasibility for nonlinear imaging in biological tissues. While the optimization of nonlinear…
Real-valued band structures are foundational to analyzing periodic systems within the Hermitian description and have been experimentally well-established over recent decades. In contrast, non-Hermitian systems exhibit complex band…
We propose a novel framework for joint magnetic resonance image reconstruction and uncertainty quantification using under-sampled k-space measurements. The problem is formulated as a Bayesian linear inverse problem, where prior…