Related papers: Super Periodic Potential
We introduce a new exactly solvable model in quantum mechanics that describes the propagation of particles through a potential field created by regularly spaced $\delta'$-type point interactions, which model the localized dipoles often…
We use coupled-mode theory to describe the scattering of a surface-plasmon polariton (SPP) from a square wave grating (Bragg grating) of finite extension written on the surface of either a metal-dielectric interface or a…
A known general class of superintegrable systems on 2D spaces of constant curvature can be defined by potentials separating in (geodesic) polar coordinates. The radial parts of these potentials correspond either to an isotropic harmonic…
A crossing symmetric $\pi N$ scattering amplitude is constructed through a complete attachment of two external pions to the dressed nucleon propagator of an underlying $\pi N$ potential model. Our formulation automatically provides…
A pair of scattering potentials are called $\alpha$-equivalent if they have identical scattering properties for incident plane waves with wavenumber $k\leq\alpha$ (energy $k^2\leq\alpha^2$.) We use a recently developed multidimensional…
We present mathematical theory for understanding the transmission spectra of heterogeneous materials formed by generalised Fibonacci tilings. Our results, firstly, characterise super band gaps, which are spectral gaps that exist for any…
A self-contained discussion of integral equations of scattering is presented in the case of centrally-symmetric potentials in one dimension, which will facilitate the understanding of more complex scattering integral equations in two and…
We consider the rationally extended exactly solvable Eckart potentials which exhibit extended shape invariance property. These potentials are isospectral to the conventional Eckart potential. The scattering amplitude for these rationally…
We propose a fast method for high order approximation of potentials of the Helmholtz type operator Delta+kappa^2 over hyper-rectangles in R^n. By using the basis functions introduced in the theory of approximate approximations, the cubature…
We develop direct and inverse scattering theory for one-dimensional Schroedinger operators with steplike potentials which are asymptotically close to different finite-gap periodic potentials on different half-axes. We give a complete…
A fast method for the computation of layer potentials that arise in acoustic scattering is introduced. The principal idea is to split the singular kernel into a smooth and a local part. The potential due to the smooth part is computed…
We describe one-dimensional stationary scattering of a two-component wave field by a non-Hermitian matrix potential which features odd-$PT$ symmetry, i.e., symmetry with $(PT)^2=-1$. The scattering is characterized by a $4\times 4$ transfer…
A simple yet accurate model for the transmission of surface plasmon polaritons (SPPs) in a finite metal-insulator-metal (MIM) waveguide to the sides of the apertures is proposed and demonstrated to be more accurate than available models. It…
We show that the formalism of supersymmetric quantum mechanics applied to the solvable elliptic function potentials $V(x) = mj(j+1){sn}^2(x,m)$ produces new exactly solvable one-dimensional periodic potentials.
In the large $N_c$ approximation to $QCD$, the leading $\pp$ scattering amplitude is expressed as the sum of an infinite number of tree diagrams. We investigate the possibility that an adequate approximation at energies up to somewhat more…
We construct the hydrodynamic equations for {\em suspensions} of self-propelled particles (SPPs) with spontaneous orientational order, and make a number of striking, testable predictions:(i) SPP suspensions with the symmetry of a true {\em…
Recent advancements in optical, terahertz, and microwave systems have unveiled non-transverse optical toroidal pulses characterized by skyrmionic topologies, fractal-like singularities, space-time nonseparability, and anapole-exciting…
Quasi-crystals are intriguing as they exhibit rotational symmetry and long range ordering but lack translational symmetry. 2-dimensional metal-dielectric patterns are interesting to make use of surface plasmon polariton (SPP) mediated local…
Surface plasmon polariton (SPP) as a bounded mode on a metal/dielectric interface intrinsically has a definite transverse magnetic (TM) polarization that usually lacks further manipulations. However, the in-plane longitudinal components of…
We provide accurate expressions for the $s$-wave scattering length for a Gaussian potential well in one, two and three spatial dimensions. The Gaussian potential is widely used as a pseudopotential in the theoretical description of…