Related papers: From quasimodes to resonances: exponentially decay…
It is well known that when the geometry and/or coefficients allow stable trapped rays, the outgoing solution operator of the Helmholtz equation (a.k.a. the resolvent of the Laplacian) grows exponentially through a sequence of real…
The primary resonance equation in partial derivatives with external force and slowly varying frequency is derived. The leading-order term of asymptotic solution is constructed as a soliton with growing amplitude when time is large. This…
We give an elementary proof of weighted resolvent bounds for semiclassical Schr\"odinger operators in dimension two. We require the potential function to be Lipschitz with long range decay. The resolvent norm grows exponentially in the…
Exceptional points (EPs) have been widely studied in quantum mechanics, condensed matter physics, optics and photonics. However, their potential in acoustics has only recently been recognized due to the rapid development of acoustic…
We consider the Dirichlet Laplacian in a three-dimensional waveguide that is a small deformation of a periodically twisted tube. The deformation is given by a bending and an additional twisting of the tube, both parametrized by a coupling…
We consider one-dimensional systems in the presence of a quasi-periodic perturbation, in the analytical setting, and study the problem of existence of quasi-periodic solutions which are resonant with the frequency vector of the…
In the presence of non-minimal gravitational couplings, matter field perturbations on a static black hole spacetime may develop unphysical poles in their linearized equations. Physical solutions confined in the domain between the event…
We study the supersymmetric partners of the harmonic oscillator with an infinite potential barrier at the origin and obtain the conditions under which it is possible to add levels to the energy spectrum of these systems. It is found that…
The quasi-bound modes localized on stable periodic ray orbits of dielectric micro-cavities are constructed in the short-wavelength limit using the parabolic equation method. These modes are shown to coexist with irregularly spaced "chaotic"…
Subwavelength resonators are small scaled objects that exhibit contrasting medium properties (eigher in intensity or sign) while compared to the ones of a uniform background. Such contrasts allow them to resonate at specific frequencies.…
We derive quantitative bounds for eigenvalues of complex perturbations of the indefinite Laplacian on the real line. Our results substantially improve existing results even for real-valued potentials. For $L^1$-potentials, we obtain optimal…
Starting from a dynamical system $(\Omega,G)$, with $G$ a generic topological group, we devise algorithms that generate families of patterns in the Euclidean space, which densely embed $G$ and on which $G$ acts continuously by rigid shifts.…
The resonances for the Wigner-von Neumann type Hamiltonian are defined by the periodic complex distortion in the Fourier space. Also, following Zworski, we characterize resonances as the limit points of discrete eigenvalues of the…
We consider 1-D quasi-periodic Frenkel-Kontorova models. We study the existence of equilibria whose frequency (i.e. the inverse of the density of deposited material) is resonant with the frequencies of the substratum. We study perturbation…
In the absence of a half-bound state, a compactly supported potential of a Schr\"odinger operator on the line is determined up to a translation by the zeros and poles of the meropmorphically continued left (or right) reflection coefficient.…
The subject of the article is linear systems of wave equations on cosmological backgrounds with convergent asymptotics. The condition of convergence corresponds to the requirement that the second fundamental form, when suitably normalised,…
Quasinormal modes of asymptotically AdS black holes can be interpreted as poles of retarded correlators in the dual gauge theory. To determine the response of the system to small external perturbations it is not enough to know the location…
In this work we establish existence and multiplicity of solutions for elliptic problem with nonlinear boundary conditions under strong resonance conditions at infinity. The nonlinearity is resonance at infinity and the reso- nance phenomena…
We prove optimal high-frequency resolvent estimates for perturbations of the Laplacian by large long-range magnetic and electric potentials in all dimensions $n\ge 3$. As an application, we prove dispersive estimates for the corresponding…
Overlapping resonances are shown to provide new insights into the extent of decoherence experienced by a system superposition state in the regime of strong system- environment coupling. As an example of this general approach, a generic…