Related papers: Inverse scattering on the quantum graph -- Edge mo…
We establish an upper bound on the spectral gap for compact quantum graphs which depends only on the diameter and total number of vertices. This bound is asymptotically sharp for pumpkin chains with number of edges tending to infinity.
It is now straightforward to carry out S-matrix to potential inversion over a very wide range of energies and for a wide range of projectile-target combinations. Inversion is possible in many cases involving spin. IP inversion also permits…
The famous question of Mark Kac "Can one hear the shape of a drum?" addressing the unique connection between the shape of a planar region and the spectrum of the corresponding Laplace operator can be legitimately extended to scattering…
We investigate Scattering amplitudes of the reversible $\theta$-exact Seiberg-Witten (SW) map based noncommutative (NC) quantum electrodynamics, and show explicitly the SW map invariance for all tree-level NCQED $2\to2$ proceses, including…
We characterize all bounded Hankel operators $\Gamma $ such that $\Gamma^*\Gamma$ has finite spectrum. We identify spectral data corresponding to such operators and construct inverse spectral theory including the characterization of these…
In this paper we consider the inverse scattering problem at a fixed energy for the Schr\"odinger equation with a long-range potential in $\ere^d, d\geq 3$. We prove that the long-range part can be uniquely reconstructed from the leading…
We study quantum scattering theory off $n$ point inhomogeneities ($n\in\bbN$) in three dimensions. The inhomogeneities (or generalized point interactions) positioned at $\{\xi_1,...,\xi_n\}\subset\bbR^3$ are modeled in terms of the $n^2$…
The matrix Schr\"odinger equation is considered on the half line with the general selfadjoint boundary condition at the origin described by two boundary matrices satisfying certain appropriate conditions. It is assumed that the matrix…
The spectral properties of the Laplacian on a class of quantum graphs with random metric structure are studied. Namely, we consider quantum graphs spanned by the simple $\ZZ^d$-lattice with $\delta$-type boundary conditions at the vertices,…
A condition, at which the one-dimensional inverse power potential becomes reflectionless during propagation through it of a plane wave, is obtained on the basis of SUSY QM methods. A scattering of a particle on spherically symmetric inverse…
This work investigates the scattering coefficients for inverse medium scattering problems. It shows some fundamental properties of the coefficients such as symmetry and tensorial properties. The relationship between the scattering…
We study the energy spectrum and persistent current of charge carriers confined in a graphene quantum ring geometry of radius $R$ and width $w$ subjected to a magnetic flux. We consider the case where the crystal symmetry is locally…
We explicitly calculate the scattering matrix at energy zero for attractive, radial and homogeneous long-range potentials. This proves a conjecture by Derezinski and Skibsted.
Scattering from a non-smooth random field on the time domain is studied for plane waves that propagate simultaneously through the potential in variable angles. We first derive sufficient conditions for stochastic moments of the field to be…
This paper devotes to providing rigorous theoretical analysis of the wellposedness of the direct problem and the uniqueness of the inverse problem of electromagnetic scattering in a parallel-plate waveguide. The direct problem is reduced to…
In the present paper we describe a method for solving inverse problems for the Helmholtz equation in radially-symmetric domains given multi-frequency data. Our approach is based on the construction of suitable trace formulas which relate…
Quantum graphs have attracted attention from mathematicians for some time. A quantum graph is defined by having a Laplacian on each edge of a metric graph and imposing boundary conditions at the vertices to get an eigenvalue problem. A…
A novel numerical method for solving inverse scattering problem with fixed-energy data is proposed. The method contains a new important concept: the stability index of the inversion problem. This is a number, computed from the data, which…
In this paper we consider an inverse problem for the $n$-dimensional random Schr\"{o}dinger equation $(\Delta-q+k^2)u = 0$. We study the scattering of plane waves in the presence of a potential $q$ which is assumed to be a Gaussian random…
In this tutorial paper, we consider the problem of electromagnetic scattering by a bounded two-dimensional dielectric object, and discuss certain interesting properties of the scattered field. Using the electric field integral equation,…