Related papers: The surprising connection between exactly solved l…
A lattice Maxwell system is developed with gauge-symmetry, symplectic structure and discrete space-time symmetry. Noether's theorem for Lie group symmetries is generalized to discrete symmetries for the lattice Maxwell system. As a result,…
We prove a complexity dichotomy theorem for a class of Holant problems on planar 3-regular bipartite graphs. The complexity dichotomy states that for every weighted constraint function $f$ defining the problem (the weights can even be…
Starting from a simple discrete model which exhibits a supersymmetric invariance we construct a local, interacting, two-dimensional Euclidean lattice theory which also admits an exact supersymmetry. This model is shown to correspond to the…
The interaction of moving discrete solitons with a linear Gaussian defect is investigated. Solitons with profiles varying from hyperbolic secant to exponentially localized are considered such that the mobility of soliton is maintained; the…
We present a robust scheme for solving the electrokinetic equations. This goal is achieved by combining the lattice-Boltzmann method (LB) with a discrete solution of the convection-diffusion equation for the different charged and neutral…
Some recent developments in the study of exactly solved lattice models in statistical mechanics are briefly reviewed. These include work with Debbie Bennett-Wood and Aleks Owczarek on polymers at surfaces (cond-mat/9805148) and with…
We explore a new type of discretizations of lattice dynamical models of the Klein-Gordon type relevant to the existence and long-term mobility of nonlinear waves. The discretization is based on non-holonomic constraints and is shown to…
This paper investigates the well-posedness of the inhomogeneous Boltzmann and Landau equations in critical function spaces, a fundamental open problem in kinetic theory. We develop a new analytical framework to establish local…
We analyze lattice Hamiltonian systems whose global symmetries have 't Hooft anomalies. As is common in the study of anomalies, they are probed by coupling the system to classical background gauge fields. For flat fields (vanishing field…
A framework is introduced which explains the existence and similarities of most exact solutions of the Einstein equations with a wide range of sources for the class of hypersurface-homogeneous spacetimes which admit a Hamiltonian…
A strongly correlated electron system with controlled hopping, in the line of the recently proposed generalized Hubbard models as candidates for high T_c-superconductors, is considered. The model along with a whole class of such systems are…
In this paper a review is given of a class of sub-models of both approaches, characterized by the fact that they can be solved exactly, highlighting in the process a number of generic results related to both the nature of pair-correlated…
Recently the neglected issue of the causal structure in the flat spacetime approach to Einstein's theory of gravity has been substantially resolved. Consistency requires that the flat metric's null cone be respected by the null cone of the…
We establish unique continuation for various discrete nonlinear wave equations. For example, we show that if two solutions of the Toda lattice coincide for one lattice point in some arbitrarily small time interval, then they coincide…
We show that one can define through the symmetry approach a procedure to check the linearizability of a difference equation via a point or a discrete Cole-Hopf transformation. If the equation is linearizable the symmetry provides the…
We compare cosmologic and spherically symmetric solutions to metric and Palatini versions of vector Horndeski theory. It appears that Palatini formulation of the theory admits more degrees of freedom. Specifically, homogeneous isotropic…
We recently introduced a class of ${\mathbb{Z}}_N$ graded discrete Lax pairs and studied the associated discrete integrable systems (lattice equations). In particular, we introduced a subclass, which we called "self-dual". In this paper we…
A detailed study of a model for strongly-interacting fermions with exclusion rules and lattice $\mathcal N=2$ supersymmetry is presented. A submanifold in the space of parameters of the model where it is Bethe-ansatz solvable is identified.…
The question of well-posedness of the generalized focusing Ablowitz-Ladik and Discrete Nonlinear Schr\"{o}dinger equations with \textit{nonzero} boundary conditions on the infinite lattice is far less understood than in the case where the…
We study the root of unity limit of the lens elliptic gamma function solution of the star-triangle relation, for an integrable model with continuous and discrete spin variables. This limit involves taking an elliptic nome to a primitive…