Related papers: Quantum integrability in two-dimensional systems w…
Abstarct: Boundary effects caused by the boundary interactions in various integrable field theories on a half line are discussed at the classical as well as the quantum level. Only the so-called ``integrable" boundary interactions are…
A Lagrangian approach is proposed and developed to study defects within affine Toda field theories. In particular, a suitable Lax pair is constructed together with examples of conserved charges. It is found that only those models based on…
We consider bosonized $QCD_2$, and prove that after rewritting the theory in terms of gauge invariant fields, there exists an integrability condition valid for the quantum theory as well. Furthermore, performing a duality type…
The concept of integrable boundary conditions is applied to hydrodynamic type systems. Examples of such boundary conditions for dispersionless Toda systems are obtained. The close relation of integrable boundary conditions with integrable…
In this paper we study various aspects of classical solutions to the affine Toda equations on a half-line with integrable boundary conditions. We begin by finding conditions that the theory has a stable vacuum by finding a Bogomolny bound…
The purpose of this talk is to address a couple of simple-sounding questions: what boundary conditions are compatible with (a) Classical integrability? (b) Quantum integrability?
Active control of quantum systems enables diverse applications ranging from quantum computation to manipulation of molecular processes. Maximum speeds and related bounds have been identified from uncertainty principles and related…
The integrability of the Bukhvostov-Lipatov four-fermion model is investigated. It is shown that the classical model possesses a current of Lorentz spin 3, conserved both in the bulk and on the half-line for specific types of boundary…
The sine-Gordon model on the half-line with a dynamical boundary introduced by Delius and one of the authors is considered at quantum level. Classical boundary conditions associated with classical integrability are shown to be preserved at…
We make an attempt to map the integrable boundary conditions for 2 dimensional non-linear O(N) $\sigma$-models. We do it at various levels: classically, by demanding the existence of infinitely many conserved local charges and also by…
The one loop quantum corrections to the classical reflection factor of the sinh-Gordon model are calculated partially for general boundary conditions. The model is studied under boundary conditions which are compatible with integrability,…
In this contribution, we discuss three situations in which complete integrability of a three dimensional classical system and its quantum version can be achieved under some conditions. The former is a system with axial symmetry. In the…
We consider an integrable model of a one-dimensional mesoscopic ring with the conduction electrons coupled by a spin exchange to a magnetic impurity. A symmetry analysis based on a Bethe Ansatz solution of the model reveals that the current…
We associate bicomplexes with several integrable models in such a way that conserved currents are obtained by a simple iterative construction. Gauge transformations and dressings are discussed in this framework and several examples are…
The inhomogeneity of the media or the external forces usually destroy the integrability of a system. We propose a systematic construction of a class of quantum models, which retains their exact integrability inspite of their explicit…
We establish the equivalence of a 2D contour dynamics to the dispersionless limit of the integrable Toda hierarchy constrained by a string equation. Remarkably, the same hierarchy underlies 2D quantum gravity.
In this work, we present a modification of explicit Runge-Kutta temporal integration schemes that guarantees the preservation of any locally-defined quasiconvex set of bounds for the solution. These schemes operate on the basis of a…
For a disordered two-dimensional model of a topological insulator (such as a Kane-Mele model with disordered potential) with small coupling of spin invariance breaking term (such as the Rashba coupling), it is proved that the spin edge…
Basic notions regarding classical integrable systems are reviewed. An algebraic description of the classical integrable models together with the zero curvature condition description is presented. The classical r-matrix approach for discrete…
We prove that for translationally invariant quantum spin chains with finite-range interactions, the existence of a specific conservation law known as the Reshetikhin condition implies the presence of infinitely many local conserved…