Related papers: Reflection-Transmission Algebras
We identify the poles and zeros of the scattering matrix of a simple quantum graph by means of systematic measurement and analysis of Wigner, transmission, and reflection complex time delays. We examine the ring graph because it displays…
A complete one-dimensional scattering of a spinless particle on a time-independent potential barrier is considered. To describe separately transmitted and reflected particles in the corresponding subsets of identical experiments, we…
Properties of relative traces and symmetrizing forms on chains of cyclotomic and affine Hecke algebras are studied. The study relies on a use of bases of these algebras which generalize a normal form for elements of the complex reflection…
We give a pedagogical introduction to time-independent scattering theory in one dimension focusing on the basic properties and recent applications of transfer matrices. In particular, we begin surveying some basic notions of potential…
We apply the concept of reflection-transmission (RT) algebra, originally developed in the context of integrable systems in 1+1 space-time dimensions, to the study of finite temperature quantum field theory with impurities in higher…
We show that periodically doped, flat surfaces can act as reflective diffraction gratings for atomic and molecular matter waves. The diffraction element is realized by exploiting that charged dopants locally suppress quantum reflection from…
The scattering properties of quantum particles on fractal potentials at different stages of fractal growth are obtained by means of the transfer matrix method. This approach can be easily adopted for project assignments in introductory…
A topological description of various generalized function algebras over corresponding basic locally convex algebras is given. The framework consists of algebras of sequences with appropriate ultra(pseudo)metrics defined by sequences of…
Based on recent results obtained by the authors on the inverse scattering method of the vector nonlinear Schr\"odinger equation with integrable boundary conditions, we discuss the factorization of the interactions of N-soliton solutions on…
In this paper we prove an $\infty$-categorical version of the reflection theorem of Ad\'amek-Rosick\'y. Namely, that a full subcategory of a presentable $\infty$-category which is closed under limits and $\kappa$-filtered colimits is a…
For any given finite abelian group, we give factorizations of the group determinant in the group algebra of any subgroup. The factorizations are an extension of Dedekind's theorem. The extension leads to a generalization of Dedekind's…
In this paper, we describe the irreducible representations and give a dimension formula for the Framisation of the Temperley-Lieb algebra. We then prove that the Framisation of the Temperley-Lieb algebra is isomorphic to a direct sum of…
The aim of this paper is to introduce and study a large class of $\mathfrak{g}$-module algebras which we call factorizable by generalizing the Gauss factorization of (square or rectangular) matrices. This class includes coordinate algebras…
We present a one-dimensional scattering theory which enables us to describe a wealth of effects arising from the coupling of the motional degree of freedom of scatterers to the electromagnetic field. Multiple scattering to all orders is…
We enumerate factorizations of a Coxeter element in a well generated complex reflection group into arbitrary factors, keeping track of the fixed space dimension of each factor. In the infinite families of generalized permutations, our…
This work continues the development of the raytracing method of [1] for computing the scattered fields from metasurfaces characterized by locally periodic reflection and transmission coefficients. In this work, instead of describing the…
A topological version of Levinson's theorem is presented. Its proof relies on a C*-algebraic framework which is introduced in detail. Various scattering systems are considered in this framework, and more coherent explanations for the…
Proceeding from optical analogy we propose a new physical interpretation of unitarity saturation leading to antishadowing as a reflective scattering. This interpretation of antishadowing is related to the non-perturbative aspects of strong…
We review recent progress in analysing wave scattering in systems with both intrinsic chaos and/or disorder and internal losses, when the scattering matrix is no longer unitary. By mapping the problem onto a nonlinear supersymmetric…
We will present an algebra describing a mixed paraparticle model, known in the bibliography as "The Relative Parabose Set (\textsc{Rpbs})". Focusing in the special case of a single parabosonic and a single parafermionic degree of freedom…