Related papers: Scattering for time periodic Hamiltonians on graph…
We study scattering for the linear Helmholtz operator in two dimensions and develop a technique, which can be used to ascertain scattering of a given incident wave from very regular inhomogeneities. This technique is then applied to a…
We develop direct scattering theory for one-dimensional Schr\"odinger operators with steplike potentials, which are asymptotically close to different Bohr almost periodic infinite-gap potentials on different half-axes.
We consider the scattering theory for the Schrodinger equation with $-\Delta -|x|^{\alpha}$ as a reference Hamiltonian, for $0< \alpha \leq 2$, in any space dimension. We prove that when this Hamiltonian is perturbed by a potential, the…
We construct a scattering theory for harmonic one-forms on Riemann surfaces, obtained from boundary value problems involving systems of curves and the jump problem. We obtain an explicit expression for the scattering matrix in terms of…
We describe the spectral theory of the adjacency operator of a graph which is isomorphic to homogeneous trees at infinity. Using some combinatorics, we reduce the problem to a scattering problem for a finite rank perturbation of the…
The theory of scattering of atom pairs in a periodic potential is presented for the case of different atoms. When the scattering dynamics is restricted to the lowest Bloch band of the periodic potential, a separation in relative and average…
In this paper we consider Schr\"oodinger operators with potentials of order zero on asymptotically conic manifolds. We prove the existence and the completeness of the wave operators with a naturally defined free Hamiltonian.
We report on the recent construction of a scattering theory for Maxwell potentials on curved spacetimes.
We study quantum walks on general graphs from the point of view of scattering theory. For a general finite graph we choose two vertices and attach one half line to each. We are interested in walks that proceed from one half line, through…
We consider a scattering theory for convolution operators on $\mathcal{H}=\ell^2(\mathbb{Z}^d; \mathbb{C}^n)$ perturbed with a long-range potential $V:\mathbb{Z}^d\to\mathbb{R}^n$. One of the motivating examples is discrete Schr\"odinger…
The group theoretical treatment of bound and scattering state problems is extended to include band structure. We show that one can realize Hamiltonians with periodic potentials as dynamical symmetries, where representation theory provides…
The aim of the lecture is to briefly describe the mathematical background of scattering theory for two- and three-particle quantum systems. We discuss basic objects of the theory: wave and scattering operators and the corresponding…
We study the theory of scattering for a class of Hartree type equations with long range interactions in space dimension n > 2, including Hartree equations with potential V(x) = lambda |x|^{- gamma} with gamma < 1. For 1/2 < gamma < 1 we…
We analyze the scattering sector of the Hamiltonians for both gapless and gapped graphene in the presence of a charge impurity using the 2D Dirac equation, which is applicable in the long wavelength limit. We show that for certain range of…
We consider the scattering for the operator $H=H_o+V$, where the unperturbed operator $H_o$ is not assumed to be elliptic and the potential $V$ is anisotropic. Under some conditions on $H_o$ and $V$ we show that the wave operators for $H_o,…
The fundamental quantities of potential scattering theory are generalized to accommodate long-range interactions. New definitions for the scattering amplitude and wave operators valid for arbitrary interactions including potentials with a…
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…
Starting with the Dirac equation outside the event horizon of a non-extreme Kerr black hole, we develop a time-dependent scattering theory for massive Dirac particles. The explicit computation of the modified wave operators at infinity is…
We define, prove the existence and obtain explicit expressions for classical time delay defined in terms of sojourn times for abstract scattering pairs (H_0,H) on a symplectic manifold. As a by-product, we establish a classical version of…
There has been quite some activity and progress concerning spectral asymptotics of random operators that are defined on percolation subgraphs of different types of graphs. In this short survey we record some of these results and explain the…