Related papers: Scattering poles for asymptotically hyperbolic man…

Acoustics recently became a versatile platform for discovering novel physical effects and concepts at a relatively simple technological level. On this way, single resonators and the structure of their resonant modes play a central role and…

We study meson-meson scattering in a soluble model which describes asymptotically free mesons and confined quark-antiquark pairs via coupled channels. Concretely, the two scattered mesons are assumed to interact through s-channel…

Scattering poles correspond to non-trivial scattered fields in the absence of incident waves and play a crucial role in the study of wave phenomena. These poles are complex wavenumbers with negative imaginary parts. In this paper, we prove…

We develop the complex scaling method for the Dirichlet Laplacian in a domain with asymptotically cylindrical end. We define resonances as discrete eigenvalues of non-selfadjoint operators, obtained as deformations of the selfadjoint…

We construct a semi-classical parametrix for the Laplacian on non-trapping asymptotically hyperbolic manifolds, which generalizes the construction of Melrose, Sa Barreto and Vasy. As applications, we obtain high energy resolvent estimates…

We study the scattering poles of $\sqrt{-\Delta} + V$, where $V$ is a compactly supported, bounded and complex valued potential. We show that the resolvent operator $ \chi R_V \chi$ has a meromorphic continuation to the whole Riemannian…

We revisit scattering of electromagnetic waves from metallic and semiconducting cylinders in the framework of complex angular momentum techniques. We prove that "resonant surface polariton modes" are generated by a unique surface wave, i.e.…

In this paper, the scattering and spectral theory of $H=\Delta_g+V$ is developed, where $\Delta_g$ is the Laplacian with respect to a scattering metric $g$ on a compact manifold $X$ with boundary and $V\in C^\infty(X)$ is real; this extends…

In this paper we describe the resonances of the singular perturbation of the Laplacian on the half space $\Omega =\mathbb R^3_+$ given by the self-adjoint operator named $\delta$-interaction. We will assume Dirichlet or Neumann boundary…

We establish soliton-like asymptotics for finite energy solutions to the Dirac equation coupled to a relativistic particle. Any solution with initial state close to the solitary manifold, converges in long time limit to a sum of traveling…

We prove general representation formulas for strongly continuous cosine and sine operator families in terms of scattering resonances of their generators. This generalizes known results related to decay, growth and oscillatory behavior of…

We show that the complex absorbing potential (CAP) method for computing scattering resonances applies to an abstractly defined class of black box perturbations of the Laplacian in $\mathbb{R}^n$ which can be analytically extended from…

We assign some kind of invariant manifolds to a given integrable PDE (its discrete or semi-discrete variant). First, we linearize the equation around its arbitrary solution $u$. Then we construct a differential (respectively, difference)…

In general, discrete eigenstates such as resonances are represented by poles of the scattering amplitude, analytically continued to the complex energy plane. In multi-channel scattering, however, the Riemann surface becomes more…

We prove high energy estimates for the boundary values of the weighted resolvent of the Laplacian on an asymptotically hyperbolic manifold. Our point is to use weights that fit the pseudo-differential calculus associated with the…

We establish soliton-like asymptotics for finite energy solutions to the Schr\"odinger equation coupled to a nonrelativistic classical particle. Any solution with initial state close to the solitary manifold, converges to a sum of traveling…

We introduce an abstract class of bosonic QFT Hamiltonians and study their spectral and scattering theories. These Hamiltonians are of the form $H=\d\G(\omega)+ V$ acting on the bosonic Fock space $\G(\ch)$, where $\omega$ is a massive…

Let $X$ be a convex co-compact hyperbolic surface and let $\delta$ be the Hausdorff dimension of the limit set of the underlying discrete group. We show that the density of the resonances of the Laplacian in strips ${\sigma\leq \re(s) \leq…

We prove a dynamical wave trace formula for asymptotically hyperbolic (n+1) dimensional manifolds with negative (but not necessarily constant) sectional curvatures which equates the renormalized wave trace to the lengths of closed…

Let $X$ be a two-dimensional smooth manifold with boundary $S^{1}$ and $Y=[1,\infty)\times S^{1}$. We consider a family of complete surfaces arising by endowing $X\cup_{S^{1}}Y$ with a parameter dependent Riemannian metric, such that the…