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This is the first in a series of papers on scattering theory for one-dimensional Schr\"odinger operators with highly singular potentials $q\in H^{-1}(R)$. In this paper, we study Miura potentials $q$ associated to positive Schr\"odinger…
Scattering of time-harmonic plane wave by two parallel semi-infinite rows, but with staggered edges, is considered on square lattice. The condition imposed on the semi-infinite rows is a discrete analogue of Neumann boundary condition. A…
The $L_\infty$-algebra approach to scattering amplitudes elegantly describes the nontrivial part of the $S$-matrix but fails to take into account the trivial part. We argue that the trivial contribution to the $S$-matrix should be accounted…
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…
In this work we study the inverse scattering problem for the selfadjoint matrix Schrodinger operator on the half line. We provide the necessary and sufficient conditions for the solvability of the inverse scattering problem.
This is the first of two subsequent publications where the probability distribution of delay-times in scattering of wave packets is discussed. The probability distribution is expressed in terms of the on-shell scattering matrix, the…
An ordinary differential operator of the fourth order with coefficients converging at infinity sufficiently rapidly to constant limits is considered. Scattering theory for this operator is developed in terms of special solutions of the…
We consider the spectral theory for discrete Schr\"odinger operators on the hexagonal lattice and their inverse scattering problem. We give a procedure for reconstructing the compactly supported potential from the scattering matrix for all…
For the eigenvalues of principal submatrices of stochastically evolving Wigner matrices, we construct and study the edge scaling limit: a random decreasing sequence of continuous functions of two variables, which at every point has the…
We present a new approach, based on graphon theory, to finding the limiting spectral distributions of general Wigner-type matrices. This approach determines the moments of the limiting measures and the equations of their Stieltjes…
For scattering systems consisting of a (family of) maximal dissipative extension(s) and a selfadjoint extension of a symmetric operator with finite deficiency indices, the spectral shift function is expressed in terms of an abstract…
We present a solution method for the inverse scattering problem for integrable two-dimensional relativistic quantum field theories, specified in terms of a given massive single particle spectrum and a factorizing S-matrix. An arbitrary…
The goal of this work is threefold. First, we give an expression of the most general five point integral on M_{0,n} in terms of Chebyshev polynomials. Second, we choose a special kinematics that transforms the polynomial form of the…
In this paper, we study the scattering theory of a class of continuum Schr\"{o}dinger operators with random sparse potentials. The existence and completeness of wave operators are proven by establishing the uniform boundedness of modified…
We study resolvent estimates, spectral theory and long time dispersive properties of scalar and matrix Schr\"odinger-type operators on $\mathbb{H}^{n+1}$ for $n \geq 1$.
The Marchenko method is developed in the inverse scattering problem for a linear system of first-order differential equations containing potentials proportional to the spectral parameter. The corresponding Marchenko system of integral…
We study the two--dimensional magnetic Schr\"odinger operator with a penetrable circular wall modeled by a $\delta$--interaction. Using the boundary triple approach we classify all self--adjoint extensions and obtain Krein's resolvent…
We study the spectral properties of Schr\"odinger operators on a compact connected Riemannian manifold $M$ without boundary in case that the underlying Hamiltonian system possesses certain symmetries. More precisely, if $M$ carries an…
We employ the so-called companion matrix method from computational algebraic geometry, tailored for zero-dimensional ideals, to study the scattering equations. The method renders the CHY-integrand of scattering amplitudes computable using…
We study the inverse scattering for Schr{\"o}dinger operators on locally perturbed periodic lattices. We show that the associated scattering matrix is equivalent to the Dirichlet-to-Neumann map for a boundary value problem on a finite part…