Related papers: Semiclassical Estimates for Scattering on the Real…
We present a detailed study of scattering by an amplitude-modulated potential barrier using three distinct physical frameworks: quantum, classical, and semiclassical. Classical physics gives bounds on the energy and momentum of the…
We adapt the semiclassical technique, as used in the context of instanton transitions in quantum field theory, to the description of tunneling transmissions at finite energies through potential barriers by complex quantum mechanical…
We solve inverse scattering problem for Schr\"odinger operators with compactly supported potentials on the half line. We discretize S-matrix: we take the value of the S-matrix on some infinite sequence of positive real numbers. Using this…
We present a general construction of semiglobal scattering solutions to quasilinear wave equations in a neighbourhood of spacelike infinity including past and future null infinity, where the scattering data are posed on an ingoing null cone…
We prove six theorems concerning exponentially accurate semiclassical quantum mechanics. Two of these theorems are known results, but have new proofs. Under appropriate hypotheses, they conclude that the exact and approximate dynamics of an…
We present a new semiclassical technique which relies on replacing complicated classical manifold structure with simpler manifolds, which are then evaluated by the usual semiclassical rules. Under circumstances where the original manifold…
This paper presents high-order integral equation methods for evaluation of electromagnetic wave scattering by dielectric bumps and dielectric cavities on perfectly conducting or dielectric half-planes. In detail, the algorithms introduced…
We consider semiclassical Schr\"odinger operators on the real line of the form $$H(\hbar)=-\hbar^2 \frac{d^2}{dx^2}+V(\cdot;\hbar)$$ with $\hbar>0$ small. The potential $V$ is assumed to be smooth, positive and exponentially decaying…
Manifolds with infinite cylindrical ends have continuous spectrum of increasing multiplicity as energy grows, and in general embedded resonances (resonances on the real line, embedded in the continuous spectrum) and embedded eigenvalues can…
This article is devoted to the construction of numerical methods which remain insensitive to the smallness of the semiclassical parameter for the linear Schr{\"o}dinger equation in the semiclassical limit. We specifically analyse the…
We reduce the solution of the scattering problem defined on the half-line $[0,\infty)$ by a real or complex potential $v(x)$ and a general homogenous boundary condition at $x=0$ to that of the extension of $v(x)$ to the full line that…
We consider scattering by general compactly supported semi-classical perturbations of the Euclidean Laplace-Beltrami operator. We show that if the suitably cut-off resolvent of the Hamiltonian quantizes a Lagrangian relation on the product…
We study the asymptotic behaviour of solutions to semi-classical nonlinear Schrodinger equations with a potential, for concentrating and oscillating initial data, when the nonlinearity is repulsive and the potential is a polynomial of…
We establish the local wellposedness of different type of solutions the system with different types of initial data. We find there exists a critical exponents line in space dimension 3 and critical exponents point in space dimension 4. We…
The object of study in this paper is the on-shell scattering matrix $S(E)$ of the Schr\"odinger operator with the potential satisfying assumptions typical in the theory of shape resonances. We study the spectrum of $S(E)$ in the…
Due to the chiral nature of the Dirac equation, overlying of an electrical superlattice (SL) can open new Dirac points on the Fermi-surface of the energy spectrum. These lead to novel low-excitation physical phenomena. A typical example for…
We consider quantum scattering from a compactly supported potential $q$. The semiclassical limit amounts to letting the wavenumber $k \to \infty$ while rescaling the potential as $k^2 q$ (alternatively, one can scale Planck's constant…
This paper shows how abstract resolvent estimates imply local smoothing for solutions to the Schr\"odinger equation. If the resolvent estimate has a loss when compared to the optimal, non-trapping estimate, there is a corresponding loss in…
We present a semiclassical S-matrix study of inelastic collinear electron-hydrogen scattering. A simple way to extract all necessary information from the deflection function alone without having to compute the stability matrix is described.…
The inverse scattering problem on the half-line has been studied in the literature in detail. V. Marchenko presented the solution to this problem. In this paper, the invertibility of the steps of the inversion procedure is discussed and a…