Related papers: Scattering resonances for highly oscillatory poten…
An analytic solution for an uniaxial spherical resonator is presented using the method of Debye potentials. This serves as a starting point for the calculation of whispering gallery modes (WGM) in such a resonator. Suitable approximations…
We consider the Dirichlet Laplacian in a straight three dimensional waveguide with non-rotationally invariant cross section, perturbed by a twisting of small amplitude. It is well known that such a perturbation does not create eigenvalues…
The paper studies the interaction of a longitudinal wave with transverse waves in general isotropic and unconstrained hyperelastic materials, including the possibility of dissipation. The dissipative term chosen is similar to the classical…
Hitherto, a finitely thick barrier next to a well or a rigid wall has been considered the potential of simplest shape giving rise to resonances (metastable states) in one dimension: $x \in(-\infty, \infty)$. In such a potential, there are…
Using universal predictions provided by classical soft theorems, we revisit the energy emission spectrum for gravitational scatterings of compact objects in the low-frequency expansion. We calculate this observable beyond the zero-frequency…
The amplification of disk oscillations resulting from non-linear resonant couplings between the oscillations and a warp is examined. The disks are geometrically thin and general relativistic with non-rotating central objects. By using a…
We consider the Schr\"odinger operator \[ P=h^2 \Delta_g + V \] on $\mathbb{R}^n$ equipped with a metric $g$ that is Euclidean outside a compact set. The real-valued potential $V$ is assumed to be compactly supported and smooth except at…
The non-perturbative Wegner-Houghton renormalization group is analyzed by the local potential approximation in O(N) scalar theories in d-dimensions $(3\leq d\leq 4)$. The leading critical exponents \nu are calculated in order to investigate…
We prove a structure formula for the wave operators in R^3 and their adjoints for a scaling-invariant class of scalar potentials V, under the assumption that zero is neither an eigenvalue, nor a resonance for -\Delta+V. The formula implies…
We consider a class of inflationary models with small oscillations imprinted on an otherwise smooth inflaton potential. These oscillations are manifest as oscillations in the power spectrum of primordial perturbations, which then give rise…
Recently, observations from laboratory experiments have revealed amplitude modulation of whistlers by low-frequency perturbations. We here present theoretical and simulation studies of amplitude modulated whistler solitary waves…
We study the cut-off resolvent of semiclassical Schr{\"o}dinger operators on $\mathbb{R}^d$ with bounded compactly supported potentials $V$. We prove that for real energies $\lambda^2$ in a compact interval in $\mathbb{R}_+$ and for any…
We present shape-independent upper limits to the power--bandwidth product for a single resonance in an optical scatterer, with the bound depending only on the material susceptibility. We show that quasistatic metallic scatterers can nearly…
Variational perturbation expansions have recently been used to calculate directly the strong-coupling expansion coefficients of the anharmonic oscillator. The convergence is exponentially fast with superimposed oscillations, as recently…
We present a semiclassical expansion of the smooth part of the density of states in potentials with some form of symmetry. The density of states of each irreducible representation is separately evaluated using the Wigner transforms of the…
We systematically investigate the preheating behavior of single field inflation with an oscillon-supporting potential. We compute the properties of the emitted gravitational waves (GWs) and the number density and characteristics of the…
We build a smooth real potential $V(t,x)$ on $(t_0,+\infty)\times \mathbb{R}^2$ decaying to zero as $t\to \infty$ and a smooth solution to the associated perturbed cubic Nonlinear Harmonic Oscillator whose Sobolev norms blow up…
Potential resonances are usually investigated either directly in the complex energy plane or indirectly in the complex angular momentum plane. Another formulation complementing these two is presented in this work. It is an indirect method…
Scattering off a potential is a fundamental problem in quantum physics. It has been studied extensively with amplitudes derived for various potentials. In this article, we explore a setting with no potentials, where scattering occurs off a…
We investigate nondegenerate parametric oscillations in a multimode superconducting microwave resonator that is terminated by a SQUID. The parametric effect is achieved by modulating magnetic flux through the SQUID at a frequency close to…