Related papers: A note on reflectionless Jacobi matrices

Scatterings and transport in Weyl semimetals have caught growing attention in condensed matter physics, with observables including chiral zero modes and the associated magnetoresistance and chiral magnetic effects. Measurement of electrical…

The Jacobi system on a full-line lattice is considered when it contains additional weight factors. A factorization formula is derived expressing the scattering from such a generalized Jacobi system in terms of the scattering from its…

We characterize the soliton solutions of the nonlinear Schroedinger equation on the half line with linearizable boundary conditions. Using an extension of the solution to the whole line and the corresponding symmetries of the scattering…

Using the sine-Gordon model as the prime example an alternative approach to integrable boundary conditions for a theory restricted to a half-line is proposed. The main idea is to explore the consequences of taking into account the…

We describe the complete set of pairwise non-isomorphic irreducible modules S(a) over the algebra R given by the defining relation xy-yx=yy, and the rule how they could be glued to indecomposables. Namely, we show that Ext_k^1(S(a),S(b))=0,…

The covariance matrix is well-known for its following properties: affine equivariance, additivity, independence property and full affine equivariance. Generalizing the first one leads into the study of scatter functionals, commonly used as…

This work identifies a solvable (in the sense that spectral correlation functions can be expressed in terms of orthogonal polynomials), rotationally invariant random matrix ensemble with a logarithmic weakly confining potential. The…

We introduce a class of metamaterials with uniformly balanced gain and loss associated with complex permittivity and permeability constants. The refractive index of such a balanced pseudo-passive metamaterial is real. An unbounded uniform…

Explicit solutions of the non-constant semi-dynamical reflection equation are constructed, together with suitable parametrizations of their structure matrices. Considering the semi-dynamical reflection equation with rational non-constant…

We develop the theory of a special type of scattering state in which a set of asymptotic channels are chosen as inputs and the complementary set as outputs, and there is zero reflection back into the input channels. In general an infinite…

Global stability of the systems has always been vital of importance; however, this concept has not yet been sufficiently developed for the nonlinear systems. This paper extends the Jacobian matrix so that this method be able to seek the…

In this paper it is considered a spectral density for a class of Jacobi matrices with absolutely continuous spectrum that was examined first by Moszynski. It is shown that the corresponding spectral density is equivalent to the positive…

Using the properties of random M\"{o}bius transformations, we investigate the statistical properties of the reflection coefficient in a random chain of lossy scatterers. We explicitly determine the support of the distribution and the…

The scattering matrix approach is employed to determine a joint probability density function of reflection eigenvalues for chaotic cavities coupled to the outside world through both ballistic and tunnel point contacts. Derived under…

A real persymmetric Jacobi matrix of order $n$ whose eigenvalues are $2k^2$ $(k=0, ..., n-1)$ is presented, with entries given as explicit functions of $n$. Besides the possible use for testing forward and inverse numerical algorithms, such…

We present a comprehensive treatment of relative oscillation theory for finite Jacobi matrices. We show that the difference of the number of eigenvalues of two Jacobi matrices in an interval equals the number of weighted sign-changes of the…

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…

The research on spectral inequalities for discrete Schrodinger Operators has proved fruitful in the last decade. Indeed, several authors analysed the operator's canonical relation to a tridiagonal Jacobi matrix operator. In this paper, we…

A scattering zipper is a system obtained by concatenation of scattering events with equal even number of incoming and out going channels. The associated scattering zipper operator is the unitary equivalent of Jacobi matrices with matrix…

We show that variants of the classical reflection functors from quiver representation theory exist in any abstract stable homotopy theory, making them available for example over arbitrary ground rings, for quasi-coherent modules on schemes,…