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We show that the conditions for total neutrino conversion found in [1] are equivalent to the conditions of maximal depth (parametric resonance) and ($\pi/2 + \pi k$) - phase of parametric oscillations. Therefore the effects considered in…
The small cross section of Raman scattering poses a great challenge for its direct study at the single-molecule level. By exploiting the high Franck-Condon factor of a common-mode resonance, choosing a large vibrational frequency difference…
All quark mass matrices with texture zeroes obtained through weak basis transformations are confronted with the experimental data. The reconstruction of the quark mass matrices M_u and M_d at the electroweak scale is performed in a weak…
Structures in the invariant mass distribution are often linked to unstable intermediate states or resonances. In experiments, many signals are detected which have broad, overlapping or intricate profiles, which makes their characterization…
We solve principal component regression (PCR), up to a multiplicative accuracy $1+\gamma$, by reducing the problem to $\tilde{O}(\gamma^{-1})$ black-box calls of ridge regression. Therefore, our algorithm does not require any explicit…
A fundamental and very well studied region of the Erd\"os-R\'enyi process is the phase transition at n/2 edges in which a giant component suddenly appears. We examine the process beginning with an initial graph. We further examine the…
We explain the application of a recently developed analytic continuation method to extract the electromagnetic transition form factors for the nucleon resonances ($N^*$) within a dynamical coupled-channel model of meson-baryon…
The topological effects of phonons have been extensively studied in various materials, particularly in the wide-bandgap semiconductor GaN, which has the potential to improve heat dissipation in power electronics due to its intrinsic,…
We compute analytically, for large $N$, the probability $\mathcal{P}(N_+,N)$ that a $N\times N$ Wishart random matrix has $N_+$ eigenvalues exceeding a threshold $N\zeta$, including its large deviation tails. This probability plays a…
A variational and perturbative treatment is provided for a family of generalized spiked harmonic oscillator Hamiltonians H = -(d/dx)^2 + B x^2 + A/x^2 + lambda/x^alpha, where B > 0, A >= 0, and alpha and lambda denote two real positive…
A combined experimental and theoretical study of transition matrix elements of the 6p 2Pj - 8s 2S1/2 transition in atomic Cs is reported. Measurements of the polarization-dependent two-photon excitation spectrum associated with the…
We consider the effect of electromagnetic coupling between localized surface plasmons in a metallic nanoparticle (NP) and excitons or weakly interacting electron-hole pairs in a semiconductor matrix where the NP is embedded. An expression…
We give asymptotic spectral results for Gram matrices of the form $ n^{-1}\mathcal{X}_n \mathcal{X}_n^T$ where the entries of $\mathcal{X}_n$ are dependent across both rows and columns. More precisely, they consist of short or long range…
The scalar -- isoscalar pi-pi phase shifts are analysed using a separable potential model of three coupled channels (pipi, KK and an effective 2pi2pi system). Model parameters are fitted to two sets of solutions obtained in a recent…
In this paper, we employ the Variable Phase Approach (VPA) to obtain the scattering phase shifts \( \delta(E, r) \), amplitude function \( A(r) \), and radial wavefunction \( u(r) \) for various channels involved in the astrophysical…
One-rank perturbations of Wigner matrices have been closely studied: let $P=\frac{1}{\sqrt{n}}A+\theta vv^T$ with $A=(a_{ij})_{1 \leq i,j \leq n} \in \mathbb{R}^{n \times n}$ symmetric, $(a_{ij})_{1 \leq i \leq j \leq n}$ i.i.d. with…
We introduce a new method to construct, within inverse-scattering theory, an energy-independent separable potential capable of reproducing exactly both phase shift and absorption over a predefined energy range. The approach relies on the…
Random sampling of large Markov matrices with a tunable spectral gap, a nonuniform stationary distribution, and a nondegenerate limiting empirical spectral distribution (ESD) is useful. Fix $c>0$ and $p>0$. Let $A_n$ be the adjacency matrix…
Fundamental optics such as lenses and prisms work by applying phase shifts to incoming light via the refractive index. In these macroscopic devices, many particles each contribute a miniscule phase shift, working together to impose a total…
Wave scattering in chaotic systems can be characterized by its spectrum of resonances, $z_n=E_n-i\frac{\Gamma_n}{2}$, where $E_n$ is related to the energy and $\Gamma_n$ is the decay rate or width of the resonance. If the corresponding ray…