The scattering theory of the integrable statistical models can be generalized to the case of systems with extended lines of defect. This is done by adding the reflection and transmission amplitudes for the interactions with the line of inhomegeneity to the scattering amplitudes in the bulk. The factorization condition for the new amplitudes gives rise to a set of Reflection-Transmission equatio...

The nonlinearity difference in the two passbands of a distributed-feedback semiconductor laser amplifier was studied experimentally. A theoretical explanation was given by using the transmission matrix approach. The difference of nonlinearity in the two passbands was found to be enhanced greatly by the mechanism of asymmetric facet reflection.

Noise parameters are a set of four measurable quantities which determine the noise performance radio-frequency device under test. The 2-port can be extracted by connecting 4 or more source impedances at device's input, measuring power with each connected, and then solving matrix equation. However, sources high reflection coefficients cannot used due to singularity that arises in entries matrix....

We construct an extended Hubbard model with open boundaries from a R-matrix based on the U q [Osp(2|2)] superalgebra. We study the reflection equation and find two classes of diagonal solutions. The corresponding one-dimensional open Hamiltonians are diagonalized by means of the Bethe ansatz approach.

A completion problem to recover a rational matrix function which is j-unitary on the line is treated. A Dirac type system with singularities on the semiaxis is recovered explicitly by its left reflection coefficient. The close connection between these two problems is discussed.

The scattering matrix for a perfectly conducting electrical cylinder (or a sound hard obstacle) in a waveguide is unitary. This is a well-known result which is a consequence of the conservation of power. When a numerical method is employed to approximate the reflection and transmission coefficients of the cylinder, an approximate scattering matrix can be constructed. An integral equation of the...

The Jordan-Wigner fermionization for the one-dimensional Bariev model of three coupled XY chains is formulated. The Lax operator in terms of fermion operators and the quantum R-matrix are presented explicitly. Furthermore, the graded reflection equations and their solutions are discussed.

We develop a transport theory to describe the dynamics of (weakly) localized waves in a quasi-1D tube geometry both in reflection and in transmission. We compare our results to recent experiments with microwaves and to other theories, such as random matrix theory and supersymmetric theory.