Related papers: Schwarzschild Quantum Fluctuations from Regge-Whee…
We consider the scattering theory for the defocusing energy subcritical wave equations with an inverse square potential. By employing the energy flux method we establish energy flux estimates on the light cone. Then by the characteristic…
We report on the recent construction of a scattering theory for Maxwell potentials on curved spacetimes.
Black hole perturbation theory on spherically symmetric backgrounds has been instrumental in establishing various aspects about the gravitational dynamics close to black holes, and continues to be an interesting avenue to confront current…
An integral equation method for scalar scattering in Schwarzschild spacetime is constructed. The zeroth-order and first-order scattering phase shift is obtained.
We analysis the radial equations for massive Dirac fields in Schwarzschild black hole spacetimes. Different approximation formulae under the WKB scheme are developed for the transmission probability ${\cal T}$ of the radial wavefunction…
We provide in this paper a first step to obtain the conformal scattering theory for the linearized gravity fields on the Schwarzschild spacetime by using the conformal geometric approach. We will show that the existing decay results for the…
A Regge--Wheeler analysis is performed for a novel black hole mimicker `the regular black hole with asymptotically Minkowski core', followed by an approximation of the permitted quasi-normal modes for propagating waveforms. A first-order…
We utilize three complementary approaches to pinpoint the exact form of scattering amplitudes in Schwarzschild spacetime. First, we solve the Regge-Wheeler equation perturbatively in the small-frequency regime. We use the obtained solutions…
In this paper a mathematical model is given for the scattering of an incident wave from a surface covered with microscopic small Helmholtz resonators, which are cavities with small openings. More precisely, the surface is built upon a…
A propagator for the one dimensional time-dependent Schr\"odinger equation with an asymmetric rectangular potential is obtained using the multiple-scattering theory approach. It allows for the consideration of the reflection and…
This article considers the problem of diffraction by a wedge consisting of two semi-infinite periodic arrays of point scatterers. The solution is obtained in terms of two coupled systems, each of which is solved using the discrete…
The theory of gauge-invariant non-spherical metric perturbations of Schwarzschild black hole spacetimes is now well established. Yet, as different notations and conventions have been used throughout the years, the literature on the subject…
If a quantum mechanical particle is scattered by a potential well, the wave function of the particle can propagate with negative phase time. Due to the analogy of the Schr\"odinger and the Helmholtz equation this phenomenon is expected to…
The aim of the lecture is to briefly describe the mathematical background of scattering theory for two- and three-particle quantum systems. We discuss basic objects of the theory: wave and scattering operators and the corresponding…
A simple and explicit technique for the numerical solution of the two-particle, time-dependent Schr\"{o}dinger equation is assembled and tested. The technique can handle interparticle potentials that are arbitrary functions of the…
The frequencies of quasinormal modes (QNM) for the Schwartzschild black hole are studied from the viewpoint of the particle scattering under an effective Regge-Wheeler type of potential consisting of a parabolic type one in an intermediate…
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 develop a method based on tensor networks to create localized single particle excitations on top of strongly-correlated quantum spin chains. In analogy to the problem of creating localized Wannier modes, this is achieved by optimizing…
We present a new algebraic method for solving the inverse problem of quantum scattering theory based on the Marchenko theory. We applied a triangular wave set for the Marchenko equation kernel expansion in a separable form. The separable…
We compute the propagation and scattering of linear gravitational waves off a Schwarzschild black hole using a numerical code which solves a generalization of the Zerilli equation to a three dimensional cartesian coordinate system. Since…