相关论文: New solutions to the Reflection Equation and the p…

We study an integrable quantum field theory of a single stable particle with an infinite number of resonance states. The exact $S$--matrix of the model is expressed in terms of Jacobian elliptic functions which encode the resonance poles…

We establish the exact solution of the nonlinear Schrodinger equation with a delta-function impurity, representing a point-like defect which reflects and transmits. We solve the problem both at the classical and the second quantized levels.…

We formulate a systematic construction of commuting quantum traces for reflection algebras. This is achieved by introducing two sets of generalized reflection equations with associated consistent fusion procedures. Products of their…

We derive and implement a suitable boundary condition for the kinetic description of the electrons inside a plasma, which takes into account microphysical processes inside the wall. It is based on the surface scattering kernel, which…

Absorbing boundaries are frequently employed in real-time propagation of the Schr\"odinger equation to remove spurious reflections and efficiently emulate outgoing boundary conditions. These conditions are a fundamental ingredient for an…

From the open boundary t-J model, an impurity model is constructed in which magnetic impurities of arbitrary spins are coupled to the edges of the strongly correlated electron system. The boundary R matrices are given explicitly. The…

We here put forward a new path-integral over Hilbert space and show that it reproduces quantum mechanics exactly. This approach works by optimizing the generating functional under a variation of the final state; it is hence an example of a…

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…

Scattering on the ${\cal PT}$-symmetric Coulomb potential is studied along a U-shaped trajectory circumventing the origin in the complex $x$ plane from below. This trajectory reflects ${\cal PT}$ symmetry, sets the appropriate boundary…

We study an inverse scattering problem for a generic hyperbolic system of equations with an unknown coefficient called the reflectivity. The solution of the system models waves (sound, electromagnetic or elastic), and the reflectivity…

An algebraic approach to integrable quantum field theory with a boundary (a half line) is presented and interesting algebraic equations, Reflection equations (RE) and Reflection Bootstrap equations (RBE) are discussed. The Reflection…

Uniformly distributed point sets on the unit sphere with and without symmetry constraints have been found useful in many scientific and engineering applications. Here, a novel variant of the Thomson problem is proposed and formulated as an…

A technique to reconstruct one-dimensional, reflectionless potentials and the associated quantum wave functions starting from a finite number of known energy spectra is discussed. The method is demonstrated using spectra that scale like the…

We examine and present new combinatorics for the Schur polynomials from the viewpoint of quantum integrability. We introduce and analyze an integrable six-vertex model which can be viewed as a certain degeneration model from a t-deformed…

Using the Quantum Inverse Scattering Method we construct an integrable Heisenberg-XXZ-model, or equivalently a model for spinless fermions with nearest-neighbour interaction, with defects. Each defect involves three sites with a fine tuning…

We predict a novel quantum interference based on the negative refraction across a semiconductor P-N junction: with a local pump on one side of the junction, the response of a local probe on the other side behaves as if the disturbance…

Nonlinear integrable models with two spatial and one temporal variables: Kadomtsev-Petviashvili equation and two-dimensional Toda lattice are investigated on the subject of correct formulation for boundary problem that can be solved within…

A quantum superintegrable model with reflections on the 2-sphere is introduced. Its two algebraically independent constants of motion generate a central extension of the Bannai--Ito algebra. The Schrodinger equation separates in spherical…

Integrable quantum mechanical systems for neutral particles with spin $\frac12$ and nontrivial dipole momentum are classified. It is demonstrated that such systems give rise to new exactly solvable problems of quantum mechanics with clear…

The diffraction of a plane wave by a transversely inhomogeneous isotropic nonmagnetic linearly polarized dielectric layer filled with a Kerr-type nonlinear medium is considered. The analytical and numerical solution techniques are…