相关论文: Barrier Penetration for Supersymmetric Shape-Invar…
The exact analytical solutions of the Schr\"odinger equation for the generalized symmetrical Woods-Saxon potential are examined for the scattering, bound and quasi-bound states in one dimension. The reflection and transmission coefficients…
An exact expression of the transmission probability through a finite graphene superlattice with an arbitrary number of potential barriers $n$ is derived in two cases of the periodic potential: rectangular electric potential and…
We derive the invariant imbedding equations for plane electromagnetic waves propagating in stratified magnetic media, where both dielectric and magnetic permeabilities vary in one spatial direction in an arbitrary manner. These equations…
This paper addresses the inverse obstacle scattering problem of simultaneously reconstructing the obstacle geometry and boundary conditions from multi-frequency near-field backscattering data. We first establish rigorous high-frequency…
We present a unifying framework that bridges Bayesian asymptotics and information theory to analyze the asymptotic Shannon capacity of general large-scale MIMO channels including ones with nonlinearities or imperfect hardware. We derive…
Using the formalism of extended N=4 supersymmetric quantum mechanics we consider the procedure of the construction of multi-well potentials. We demonstrate the form-invariance of Hamiltonians entering the supermultiplet, using the presented…
It is well known that the modulus of the far-field pattern (or phaseless far-field pattern) is invariant under translations of the scattering obstacle if only one plane wave is used as the incident field, so the shape but not the location…
We construct a frame of complex Gaussians for the space of $L^2(\mathbb{R}^n)$ functions. When propagated along bicharacteristics for the wave equation, the frame can be used to build a parametrix with suitable error terms. When the…
In the present manuscript, we consider the practical problem of wave interaction with a vertical wall. However, the novelty here consists in the fact that the wall can move horizontally due to a system of springs. The water wave evolution…
For distinguishable particles it is well known that Brownian motion and a Feynman-Kac functional can be used to calculate the path integral (for imaginary times) for a general class of scalar potentials. In order to treat identical…
The mechanism of superluminal traversal time through a potential well or potential barrier is investigated from the viewpoint of interference between multiple finite wave packets, due to the multiple reflections inside the well or barrier.…
In this paper we introduce the concept of super periodic potential (SPP) of arbitrary order $n$, $n \in I^{+}$, in one dimension. General theory of wave propagation through SPP of order $n$ is presented and the reflection and transmission…
We construct the general partial wave amplitude basis for the $N\to M$ scattering, which consists of Poincar\'e Clebsch-Gordan coefficients, with Lorentz invariant forms given in terms of spinor-helicity variables. The inner product of the…
We propose a parity-time symmetric dielectric-nanofilm-dielectric multilayered structure that could facilitate highly amplified transmission of optical power in the infrared spectrum. We have theoretically studied our model using the…
The present study addresses the question of total internal reflection of a plane wave from an amplifying or attenuating medium. Inspection on the expressions for the modal gain or loss of an asymmetric planar waveguide having an amplifying…
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…
In this paper a new class of radial basis functions based on hyperbolic trigonometric functions will be introduced and studied. We focus on the properties of their generalised Fourier transforms with asymptotics. Therefore we will compute…
Wave propagation and acoustic scattering problems require vast computational resources to be solved accurately at high frequencies. Asymptotic methods can make this cost potentially frequency independent by explicitly extracting the…
We consider electron transport in a ballistic multi-mode channel structure in the presence of a transversely polarized far-infrared (FIR) field. The channel structure consists of a long resonance region connected to an adiabatic widening…
We propose a system of real-space envelope function equations without fitting parameters for modeling the electronic spectrum and wave functions of a phosphorus donor atom embedded in silicon. The approach relies on the Burt-Foreman…