Related papers: Scattering resonances as viscosity limits
In even dimensional Euclidean scattering, the resonances lie on the logarithmic cover of the complex plane. This paper studies resonances for obstacle scattering in ${\mathbb R}^d$ with Dirchlet or admissable Robin boundary conditions, when…
The diffraction spectrum of coherent waves scattered from fractal supports is calculated exactly. The fractals considered are of the class generated iteratively by successive dilations and translations, and include generalizations of the…
Formulas are derived for solutions of many-body wave scattering problems by small particles in the case of acoustically soft, hard, and impedance particles embedded in an inhomogeneous medium. The limiting case is considered, when the size…
The generator coordinate method of a microscopic cluster model is developed to treat the resonance and scattering of nuclear clusters with complex scaling. We consistently derive the formulation of the complex scaling for the microscopic…
Resonances, which are also described as autoionizing or quasi-bound states, play an important role in the scattering of atoms and ions with electrons. The current article is an overview of the main methods, including a recently-proposed…
We show how the scattering phase shift, the s-wave scattering length and the p-wave scattering volume can be obtained from Riccati equations derived in variable phase theory. We find general expressions that provide upper and lower bounds…
We prove dispersive estimates in R^3 for the Schroedinger evolution generated by the Hamiltonian H = -\Delta+V, under optimal decay conditions on V, in the presence of zero energy eigenfunctions and resonances.
We study resonances of compactly supported potentials $ V_\varepsilon = W ( x, x/\varepsilon ) $ where $ W : \mathbb{R}^d \times \mathbb{R}^d / ( 2\pi \mathbb{Z}) ^d \to \mathbb{C} $, $ d $ odd. That means that $ V_\varepsilon $ is a sum of…
Infinitely rising one-dimensional potentials constitute impenetrable barriers which reflect totally any incident wave. However, the scattering by such kind of potentials is not structureless: resonances may occur for certain values of the…
In this paper, we give a polynomial lower bound for the resonances of $-\Delta$ perturbed by an obstacle in even-dimensional Euclidean spaces, $n\geq4$. The proof is based on a Poisson Summation Formula which comes from the Hadamard…
Many low energy hadrons, such as the rho, can be observed as resonances in scattering experiments. A proposal by L\"uscher enables one to determine infinite volume elastic scattering phases from the two-particle energy spectrum measured…
The need of mathematically formulate relations between composite materials' properties and its resonance response is growing. This is due the fast technological advancement in micro-material manufacturing, present in chips for instance. In…
We develop a variational method to obtain accurate bounds for the eigenenergies of H = -Delta + V in arbitrary dimensions N>1, where V(r) is the nonpolynomial oscillator potential V(r) = r^2 + lambda r^2/(1+gr^2), lambda in…
A peculiar property of complex scattering potentials is the appearance of spectral singularities. These are energy eigenvalues for certain scattering states that similarly to resonance states have infinite reflection and transmission…
Quantum resonances, i.e., metastable states with a finite lifetime, play an important role in nuclear physics and other domains. Describing this phenomenon theoretically is generally a challenging task. In this work, we combine two…
We present in detail a dispersion relation formalism for virtual Compton scattering (VCS) off the proton from threshold into the $\Delta(1232)$-resonance region. Such a formalism can be used as a tool to extract the generalized…
An S matrix approach is developed to describe elastic scattering resonances of systems where the scattered particle is asymptotically confined and the scattering potential lacks continuous symmetry. Examples are conductance resonances in…
We combine theories of scattering for linearized water waves and flexural waves in thin plates to characterize and achieve control of water wave scattering using floating plates. This requires manipulating a sixth-order partial differential…
We study graviton-graviton scattering in partial-wave amplitudes after unitarizing their Born terms. In order to apply S-matrix techniques, based on unitarity and analyticity, we introduce an S-matrix associated to this resummation that is…
We address the two-dimensional band-structure of graphene above the vacuum level in the context of discrete states immersed in the three-dimensional continuum. Scattering resonances are discovered that originate from the coupling of the…