Related papers: Body resonances for classical waves
Under certain conditions, the quantum delta-kicked harmonic oscillator displays quantum resonances. We consider an atom-optical realization of the delta-kicked harmonic oscillator, and present a theoretical discussion of the quantum…
We consider resonances for fourth order differential operators on the half-line with compactly supported coefficients. We determine asymptotics of a counting function of resonances in complex discs at large radius, describe the forbidden…
Properties of nucleon and $\Delta$ resonances are derived from a multichannel partial wave analysis. The statistical significance of pion and photo-induced inelastic reactions off protons are studied in a multichannel partial-wave analysis.
A Gelfand triplet for the Hamiltonian H of the infinite-dimensional Friedrichs model on the positive half line with Hilbert-Schmidt perturbations is constructed such that exactly the resonances (poles of the inverse of the Livsic-matrix)…
In this paper, we study the dispersive properties of the wave equation associated with the shifted Laplace-Beltrami operator on real hyperbolic spaces, and deduce Strichartz estimates for a large family of admissible pairs. As an…
We investigate dispersive estimates for the Schr\"odinger operator $H=-\Delta +V$ with $V$ is a real-valued decaying potential when there are zero energy resonances and eigenvalues in four spatial dimensions. If there is a zero energy…
We study the properties of eigenvalues and corresponding eigenfunctions generated by a defect in the gaps of the spectrum of a high-contrast random operator. We consider a family of elliptic operators $\mathcal{A}^\varepsilon$ in divergence…
We study the fourth order Schr\"odinger operator $H=(-\Delta)^2+V$ for a short range potential in three space dimensions. We provide a full classification of zero energy resonances and study the dynamic effect of each on the $L^1\to…
We study two uncoupled oscillators, horizontal and vertical, residing in rectilinear polygons (with only vertical and horizontal sides) and impacting elastically from their boundary. The main purpose of the article is to analyze the…
It is shown that for the one-dimensional quantum anharmonic oscillator with potential $V(x)= x^2+g^2 x^4$ the Perturbation Theory (PT) in powers of $g^2$ (weak coupling regime) and the semiclassical expansion in powers of $\hbar$ for…
The notion of operator resonances was introduced earlier by Al. Zamolodchikov within the framework of the conformal perturbation theory. The resonances are related to logarithmic divergences of integrals in the perturbation expansion, and…
This paper is concerned with the homogenization of the Dirichlet eigenvalue problem, posed in a bounded domain $\Omega\subset\mathbb R^2$, for a vectorial elliptic operator $-\nabla\cdot A^\epsilon(\cdot)\nabla$ with $\epsilon$-periodic…
We consider an eigenvalue problem for a divergence form elliptic operator $A_\epsilon$ with high contrast periodic coefficients with period $\epsilon$ in each coordinate, where $\epsilon$ is a small parameter. The coefficients are perturbed…
Let $(M,g)$ be a complete manifold of nonpositive scalar curvature, let $\Omega\subset M$ be a suitable domain, and let $\lambda(\Omega)$ be the first Dirichlet eigenvalue of the Laplace-Beltrami operator on $\Omega$. We prove several…
We treat the quantum dynamics of a harmonic oscillator as well as its inverted counterpart in the Schr\"odinger picture. Generally in the most papers of the literature, the inverted harmonic oscillator is formally obtained from the harmonic…
Two different methods are used to study the existence and stability of the (1+1)-dimensional $\Phi^4$ oscillon. The variational technique approximates it by a periodic function with a set of adiabatically changing parameters. An alternative…
The Stark resonance parameters for the $3a_{1}$ molecular orbital of H$_{2}$O are computed by solving a system of partial differential equations in spherical polar coordinates. The starting point of the calculation is the quantum potential…
We consider a family of second-order parabolic operators $\partial_t+\mathcal{L}_\varepsilon$ in divergence form with rapidly oscillating, time-dependent and almost-periodic coefficients. We establish uniform interior and boundary H\"older…
A model potential previously developed for the ammonia molecule is treated in a single-center partial-wave approximation in analogy with a self-consistent field method developed by Moccia. The latter was used in a number of collision…
Oscillons are localised long-lived pulsating states in the three-dimensional $\phi^4$ theory. We gain insight into the spatio-temporal structure and bifurcation of the oscillons by studying time-periodic solutions in a ball of a finite…