Related papers: How close Are Integrable and Non-integrable Models…
Understanding the relationship which integrable (solvable) models, all of which possess very special symmetry properties, have with the generic non-integrable models that are used to describe real experiments, which do not have the symmetry…
We present a quasi-integrable two-dimensional lattice equation: i.e., a partial difference equation which satisfies a criterion of integrability, singularity confinement, although it has a chaotic aspect in the sense that the degrees of its…
We introduce a new information-theoretic formulation of quantum measurement uncertainty relations, based on the notion of relative entropy between measurement probabilities. In the case of a finite-dimensional system and for any approximate…
We develop a numerical algorithm for identifying approximately conserved quantities in models perturbed away from integrability. In the long-time regime, these quantities fully determine correlation functions of local observables. Applying…
A new integrable discrete system is constructed and studied, based on the algebraization of the difference operator. The model is named the discrete generalized nonlinear Schrodinger (GNLS) equation for which can be reduced to classical…
A procedure allowing for the construction of Lorentz invariant integrable models living in d+1 dimensional space-time and with an n dimensional target space is provided. Here, integrability is understood as the existence of the generalized…
The knowledge of {\it non usual} and sometimes {\it hidden} symmetries of (classical) integrable systems provides a very powerful setting-out of solutions of these models. Primarily, the understanding and possibly the quantisation of…
This project investigates the applicability of quasi-Monte Carlo methods to Euclidean lattice systems in order to improve the asymptotic error scaling of observables for such theories. The error of an observable calculated by averaging over…
In this paper, we explore the relationship between integrability and the discrete holomorphicity of a class of complex lattice observables in the context of the Potts dense loop model and the O(n) dilute loop model. It is shown that the…
We consider deformations of the $SU(3)$ Affine Toda theory (AT) and investigate the integrability properties of the deformed theories. We find that for some special deformations all conserved quantities change to being conserved only…
We investigate the relevance of the conformal method by investigating stability issues for the Einstein-Lichnerowicz conformal constraint system in a nonlinear scalar-field setting. We prove the stability of the system with respect to…
We provide Lyapunov-like characterizations of boundedness and convergence of non-trivial solutions for a class of systems with unstable invariant sets. Examples of systems to which the results may apply include interconnections of stable…
Coupled discrete models abound in several areas of physics. Here we provide an extensive set of exact quasiperiodic solutions of a number of coupled discrete models in terms of Lame polynomials of order one and two. Some of the models…
We investigate the integrability and non-integrability of isotropic spin chains with nearest-neighbor interaction with general spin $S$ in terms of the presence or absence of local conserved quantities. We prove a dichotomy theorem that…
We consider boundary conditions compatible with discrete holomorphicity for the dilute O(n) and C_2^(1) loop models. In each model, for a general set of boundary plaquettes, multiple types of loops can appear. A generalisation of Smirnov's…
Zamolodchikov found an integrable field theory related to the Lie algebra E$_8$, which describes the scaling limit of the Ising model in a magnetic field. He conjectured that there also exist solvable lattice models based on E$_8$ in the…
The perturbed NLS equation is asymptotically integrable if the zero-order approximation to the solution is a single soliton. It is not integrable for any other zero-order solution. In the standard application of a Normal Form expansion,…
We show that solutions to the Ablowitz--Ladik system converge to solutions of the cubic nonlinear Schr\"odinger equation for merely $L^2$ initial data. Furthermore, we consider initial data for this lattice model that excites Fourier modes…
We explore various combinatorial problems mostly borrowed from physics, that share the property of being continuously or discretely integrable, a feature that guarantees the existence of conservation laws that often make the problems…
Robustness is a basic property of any control system. In the context of linear output regulation, it was proved that embedding an internal model of the exogenous signals is necessary and sufficient to achieve tracking of the desired…