Related papers: A Dynamical System Connected with Inhomogeneous 6-…
We present a derivation of the kinetic equation describing the secular evolution of spatially inhomogeneous systems with long-range interactions, the so-called inhomogeneous Landau equation, by relying on a functional integral formalism. We…
The inhomogeneous six-vertex model is a 2$D$ multiparametric integrable statistical system. In the scaling limit it is expected to cover different classes of critical behaviour which, for the most part, have remained unexplored. For general…
The Hamiltonian analysis for a 3-dimensional connection dynamics of $\frak{so}(1,2)$, spanned by $\{L_{-+},L_{-2},L_{+2}\}$ instead of $\{L_{01}, L_{02}, L_{12}\}$, is first conducted in a Bondi-like coordinate system. The symmetry of the…
This talk is inspired by two previous ICM talks, by V.Drinfeld (1986) and G.Felder (1994). Namely, one of the main ideas of Drinfeld's talk is that the quantum Yang-Baxter equation (QYBE), which is an important equation arising in quantum…
In this short note, we discuss the basic approach to computational modeling of dynamical systems. If a dynamical system contains multiple time scales, ranging from very fast to slow, computational solution of the dynamical system can be…
We study quantization of a self-interacting scalar field within the unfolded dynamics approach. To this end we find and analyze a classical unfolded system describing 4d off-shell scalar field with a general self-interaction potential. Then…
The correspondence between the integrability of classical mechanical systems and their quantum counterparts is not a 1-1, although some close correspondencies exist. If a classical mechanical system is integrable with invariants that are…
We consider the relationship between symmetries of two-dimensional autonomous dynamical system in two common formulations; as a set of differential equations for the derivative of each state with respect to time, and a single differential…
We show that the stochastic dynamics of a large class of one-dimensional interacting particle systems may be presented by integrable quantum spin Hamiltonians. Generalizing earlier work \cite{Stin95a,Stin95b} we present an alternative…
The homogeneous dynamo effect is at the root of cosmic magnetic field generation. With only a very few exceptions, the numerical treatment of homogeneous dynamos is carried out in the framework of the differential equation approach. The…
In the first part of the thesis we construct models, called integrable, in which we can perform exact computations of physical quantities. We introduce several new out-of-equilibrium models that are obtained by solving, in specific cases,…
We analyze and discuss convergence properties of a numerically exact algorithm tailored to study the dynamics of interacting two-dimensional lattice systems. The method is based on the application of the time-dependent variational principle…
We perform a In\"on\"u--Wigner contraction on Gaudin models, showing how the integrability property is preserved by this algebraic procedure. Starting from Gaudin models we obtain new integrable chains, that we call Lagrange chains,…
We present the expressions for the monodromy matrix elements of the six-vertex model in the F-basis for arbitrary Boltzmann weights. The results rely solely on the property of unitarity and Yang-Baxter relations, avoiding any specific…
We propose a dynamical matrix product ansatz describing the stochastic dynamics of two species of particles with excluded-volume interaction and the quantum mechanics of the associated quantum spin chains respectively. Analyzing consistency…
The paper deals with a dynamical system analysis related to phantom cosmological model . Here gravity is coupled to phantom scalar field having scalar coupling function and a potential. The field equations are reduced to an autonomous…
We introduce a one dimensional spin $\frac{1}{2}$ Hamiltonian with multi-site interactions, but still local. The algebra of its Hamiltonian densities resembles that of the transverse field Ising model. Using this fact we show that its…
The representation theory of the Drinfeld doubles of dihedral groups is used to solve the Yang-Baxter equation. Use of the 2-dimensional representations recovers the six-vertex model solution. Solutions in arbitrary dimensions, which are…
Integrable systems in low dimensions, constructed through the symmetry reduction method, are studied using phase portrait and variable separation techniques. In particular, invariant quantities and explicit periodic solutions are…
We study the most general form of a three dimensional classical integrable system with axial symmetry and invariant under the axis reflection. We assume that the three constants of motion are the Hamiltonian, $H$, with the standard form of…