Related papers: Differences of spectral projections and scattering…
We develop a dynamical formulation of one-dimensional scattering theory where the reflection and transmission amplitudes for a general, possibly complex and energy-dependent, scattering potential are given as solutions of a set of dynamical…
The definitions of scattering matrix and inclusive scattering matrix in the framework of formulation of quantum field theory in terms of associative algebras with involution are presented. The scattering matrix is expressed in terms of…
The main objective of this paper is to systematically develop a spectral and scattering theory for selfadjoint Schr\"odinger operators with $\delta$-interactions supported on closed curves in $\mathbb R^3$. We provide bounds for the number…
Speckle patterns are inherent features of coherent light propagation through complex media. As a result of interference, they are sensitive to multiple experimental parameters such as the configuration of disorder or the propagating…
A new method of path averaging for waves propagating in a random dilute system of identical scatterers is developed. The scattering matrix of such a system is calculated. The method systematically takes into account repeating scatterings on…
Theory of scattering of a quantum-mechanical particle on a cosmic string is developed. S-matrix and scattering amplitude are determined as functions of the flux and the tension of the string. We reveal that, in the case of the nonvanishing…
Predator-prey networks originating from different aqueous and terrestrial environments are compared to assess if the difference in environments of these networks produce any significant difference in the structure of such predator-prey…
The spectral and scattering theory for 1-dimensional Dirac operators with mass $m$ and with zero-range interactions are fully investigated. Explicit expressions for the wave operators and for the scattering operator are provided. These new…
We consider a family {P} of determinantal point processes arising in representation theory and random matrix theory. The processes live on the one-dimensional lattice and their correlation kernels correspond to projection operators in the…
We consider a quantum system S interacting with another system S and susceptible of being absorbed by S. The effective, dissipative dynamics of S is supposed to be generated by an abstract pseudo-Hamiltonian of the form H = H0 + V -- iC *…
The formalism of the scattering matrix is applied to describe the transmission properties of multilayered structures with deep variations of the refractive index and arbitrary arrangements of the layers. We show that there is an exact…
We formulate a theory of nonrelativistic scattering in one dimension based on the J-matrix method. The scattering potential is assumed to have a finite range such that it is well represented by its matrix elements in a finite subset of a…
In this paper, we investigate the spectral projection of density matrices in quantum field theory. With appropriate regularization, the spectral projectors of density matrices are expected to be well-defined. These projectors can be…
We generalise a classical example given by Krein in 1953. We compute the difference of the resolvents and the difference of the spectral projections explicitly. We further give a full description of the unitary invariants, i.e., of the…
This review revolves around the question which general distribution of scatterers (in a Euclidean space) results in a pure point diffraction spectrum. Firstly, we treat mathematical diffration theory and state conditions under which such a…
We develop the method of similar operators to study the spectral properties of unbounded perturbed linear operators that can be represented by matrices of various kinds. The class of operators under consideration includes various…
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…
We review the spectral analysis and the time-dependent approach of scattering theory for manifolds with asymptotically cylindrical ends. For the spectral analysis, higher order resolvent estimates are obtained via Mourre theory for both…
Symmetry relationships for optical observations of matter generally fall into several common scattering geometries. The 'planetary' configuration is preferred among a group of observers of extraterrestrial planets, 'laboratory' observations…
Let $H_0$, $H$ be a pair of self-adjoint operators for which the standard assumptions of the smooth version of scattering theory hold true. We give an explicit description of the absolutely continuous spectrum of the operator…