Related papers: Integrable Systems with Pairwise Interactions and …
Statistical systems composed of atoms interacting with each other trough nonintegrable interaction potentials are considered. Examples of these potentials are hard-core potentials and long-range potentials, for instance, the Lennard-Jones…
We extend the equations of motion that describe non-relativistic elastic collision of two particles in one dimension to an arbitrary associative algebra. Relativistic elastic collision equations turn out to be a particular case of these…
The duality between a class of the Davey-Stewartson type coupled systems and a class of two-dimensional Toda type lattices is discussed. For the recently found integrable lattice the hierarchy of symmetries is described. Second and third…
Relativistic systems of particles interacting pairwise at a distance (interactions not mediated by fields) in flat spacetime are studied. It is assumed that the interactions propagate at the speed of light in vacuum and that all masses are…
In this article I study pairing of two interacting particles in ideal 1D, 2D and Bethe lattices. I employ the method of recursion that has been formulated recently by Berciu et. al. to compute the pair functions in real space without…
We present a new type of integrable one-dimensional many-body systems called a one-parameter Calogero-Moser (CM) system. In the discrete level, the Lax pairs with a parameter are introduced and, of course, the discrete-time equations of…
Nenciu and Simon found that the analogue of the Toda system in the context of orthogonal polynomials on the unit circle is the defocusing Ablowitz-Ladik system. In this paper we use the CMV and extended CMV matrices, respectively, to…
We study the $C_{n}$ and $BC_{n}$ Ruijsenaars-Schneider(RS) models with interaction potential of trigonometric and rational types. The Lax pairs for these models are constructed and the involutive Hamiltonians are also given. Taking…
This article reviews the role of hidden symmetries of dynamics in the study of physical systems, from the basic concepts of symmetries in phase space to the forefront of current research. Such symmetries emerge naturally in the description…
A family of integrable $GL(NM)$ models is described. On the one hand it generalizes the classical spin Ruijsenaars--Schneider systems (the case $N=1$), and on the other hand it generalizes the relativistic integrable tops on $GL(N)$ Lie…
Photons strongly coupled to material systems constitute a novel system for studying the dynamics of non-equilibrium quantum many-body systems. We give a fully analytical description of the dynamics of photons coupled to a one-dimensional…
The two-particle models in de Sitter space-time with time-asymmetric retarded-advanced interactions are constructed. Particular cases of the field-type electromagnetic and scalar interactions are considered. The manifestly covariant…
Differential-difference integrable exponential type systems are studied corresponding to the Cartan matrices of semi-simple or affine Lie algebras. For the systems corresponding to the algebras $A_2$, $B_2$, $C_2$, $G_2$ the complete sets…
A new approach to relativistic mechanics is proposed, suitable to describe dynamics of different kinds of relativistic particles. Mathematically it is based on an application of the recent geometric theory of nonholonomic systems on fibred…
Integrable spin systems possess interesting geometrical and gauge invariance properties and have important applications in applied magnetism and nanophysics. They are also intimately connected to the nonlinear Schr\"odinger family of…
It is shown that the Calogero-Moser models based on all root systems of the finite reflection groups (both the crystallographic and non-crystallographic cases) with the rational (with/without a harmonic confining potential), trigonometric…
Integrable systems constitute an essential part of modern physics. Traditionally, to approve a model is integrable one has to find its infinitely many symmetries or conserved quantities. In this letter, taking the well known Korteweg-de…
Scientists have developed hundreds of techniques to measure the interactions between pairs of processes in complex systems. But these computational methods, from correlation coefficients to causal inference, rely on distinct quantitative…
The dynamical systems of identical particles admitting quadratic integrals of motion are classified. The relevant integrals are explicitly constructed and their relation to separation of variables in H-J equation is clarified.
Various topics concerning the entanglement of composite quantum systems are considered with particular emphasis concerning the strict relations of such a problem with the one of attributing objective properties to the constituents. Most of…