Related papers: Spectral Properties of Elementwise-Transformed Spi…
At lower energies, the resonances in scattering experiments are often isolated. The crucial parameter is the ratio of average resonance width and average mean level spacing. Towards larger energies, this parameter grows, because the…
The interference of fluorescence signals and noise remains a significant challenge in Raman spectrum analysis, often obscuring subtle spectral features that are critical for accurate analysis. Inspired by variational methods similar to…
Magnons are elementary excitations in magnetic materials and undergo nonlinear multimode scattering processes at large input powers. In experiments and simulations, we show that the interaction between magnon modes of a confined magnetic…
We study elastic N$\alpha $ scattering and produce a quantitative correlation between the range of the effective potential and the energy of the system. This allows the identification of the waves and energies for which the scattering may…
The quantitative contributions of a mixed phase-space to the mean characterizing the distribution of diagonal transition matrix elements and to the variance characterizing the distributions of non-diagonal transition matrix elements are…
Solutions SP00, SM00 and FA00 of nucleon-nucleon (NN) phase shift analyzes by Arndt et al. are used in optical model studies. The partial waves, single channels J.leq.7 and coupled channels J.leq.6, are scrutinized. The radial probability…
We consider a slow-fast Hamiltonian system with one fast angular variable (a fast phase) whose frequency vanishes on some surface in the space of slow variables (a resonant surface). Systems of such form appear in the study of dynamics of…
We investigate spectral properties of quantum graphs in the form of a periodic chain of rings with a connecting link between each adjacent pair, assuming that wave functions at the vertices are matched through conditions manifestly…
Advanced transition elements are of utmost importance in many applications of the finite element method (FEM) where a local mesh refinement is required. Considering problems that exhibit singularities in the solution, an adaptive…
We consider rank-one symmetric tensor estimation when the tensor is corrupted by Gaussian noise and the spike forming the tensor is a structured signal coming from a generalized linear model. The latter is a mathematically tractable model…
We study grand--canonical and canonical properties of the model of branched polymers proposed in \cite{adfo}. We show that the model has a fourth order phase transition and calculate critical exponents. At the transition the exponent…
We consider a spiked random matrix model obtained by applying a function entrywise to a signal-plus-noise symmetric data matrix. We prove that the largest eigenvalue of this model, which we call a transformed spiked Wigner matrix, exhibits…
A major issue in harmonic analysis is to capture the phase dependence of frequency representations, which carries important signal properties. It seems that convolutional neural networks have found a way. Over time-series and images,…
Consider the rank-1 spiked model: $\bf{X}=\sqrt{\nu}\xi \bf{u}+ \bf{Z}$, where $\nu$ is the spike intensity, $\bf{u}\in\mathbb{S}^{k-1}$ is an unknown direction and $\xi\sim \mathcal{N}(0,1),\bf{Z}\sim \mathcal{N}(\bf{0},\bf{I})$. Motivated…
Rydberg atoms have attracted considerable interest due to their huge interaction among each other and with external fields. They demonstrate characteristic scaling laws in dependence on the principal quantum number $n$ for features such as…
The reflecting features (reflected spectrum and phase) on the surface of pure-material plate depend on refractive index, extinction coefficient, incident angle, polarization direction and so on. The features, however, do not depend on a cut…
We investigate inelastic microwave photon scattering by a transmon qubit embedded in a high-impedance circuit. The transmon undergoes a charge-localization (Schmid) transition upon the impedance reaching the critical value. Due to the…
We consider $N\times N$ Gaussian random matrices, whose average density of eigenvalues has the Wigner semi-circle form over $[-\sqrt{2},\sqrt{2}]$. For such matrices, using a Coulomb gas technique, we compute the large $N$ behavior of the…
The NMR spectra of paramagnetic substances can feature shifts over thousands of ppm. In high magnetic field instruments, this corresponds to extreme offsets, which make it challenging or impossible to achieve uniform excitation without…
Electron shelving gives rise to bright and dark periods in the resonance fluorescence of a three-level atom. The corresponding incoherent spectrum contains a very narrow inelastic peak on top of a two-level-like spectrum. Using the theories…