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We investigate the Yang-Baxter algebra for $\mathrm{U}(1)$ invariant three-state vertex models whose Boltzmann weights configurations break explicitly the parity-time reversal symmetry. We uncover two families of regular Lax operators with…
Bright, saturated structural colors in birds have inspired synthesis of self-assembled, disordered arrays of assembled nanoparticles with varied particle spacings and refractive indices. However, predicting colors of assembled…
We describe how parton recombination can address the recent measurement of dynamical jet-like two particle correlations. In addition we discuss the possible effect realistic light-cone wave-functions including higher Fock-states may have on…
Non-associtive algebras is a research direction gaining much attention these days. New developments show that associative algebras and some not-associative structures can be unified at the level of Yang-Baxter structures. In this paper, we…
We find that point particles interacting with a self-dual Yang-Mills field and self-dual gravity manifestly satisfy color-kinematics duality at the level of action. In a similar way color-kinematics duality also holds for a scalar field…
Computational methods are an important tool for solving the Yang-Baxter equations(in small dimensions), for classifying (unifying) structures, and for solving related problems. This paper is an account of some of the latest developments on…
We present integrable lattice equations on a two dimensional square lattice with coupled vertex and bond variables. In some of the models the vertex dynamics is independent of the evolution of the bond variables, and one can write the…
Quadratic systems generated using Yang-Baxter equations are integrable in a sense, but we display a deterioration in the possession of the Painlev\'e property as the number of equations in each `integrable system' increases. Certain…
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 Baxterization of a two-colour generalization of the Birman--Wenzl--Murakami (BWM) algebra. Appropriately combining two RSOS-type representations of the ordinary BWM algebra, we construct representations of the two-colour…
In this paper we give an overview of exactly solved edge-interaction models, where the spins are placed on sites of a planar lattice and interact through edges connecting the sites. We only consider the case of a single spin degree of…
We studied the effect of collimation for monochromatic beams of spin waves, resulting from the refraction at the interface separating two magnetic half-planes. The collimation was observed in broad range of the angles of ncidence for…
We report on studies of Bose-Einstein correlations and color reconnection in hadronic W pair production at LEP. Bose-Einstein correlations between identical particles from the decay of different W's are studied by comparing the particle…
A modified Rota-Baxter algebra is an algebra equipped with an operator that satisfies the modified Yang-Baxter equation. In this paper, we define the cohomology of a modified Rota-Baxter algebra with coefficients in a suitable bimodule. We…
Since it was first discussed by Baxter in 1970, the three coloring model has been studied in several contexts, from frustrated magnetism to superconducting devices and glassiness. In presence of interactions, when the model is no longer…
We consider a process in which there are p-species of particles, i.e. A_1,A_2,...,A_p, on an infinite one-dimensional lattice. Each particle $A_i$ can diffuse to its right neighboring site with rate $D_i$, if this site is not already…
Nano- to micro-sized particles with differently charged surface areas exhibit complex interaction patterns, characterized by both opposite-charge attraction and like-charge repulsion. While several successful models have been proposed in…
We have succeeded to develop a model pair interaction which when added to a system of interacting particles can be tuned to arrange the interacting objects into sheets. The interaction is based on the decomposition of the dipole-dipole…
Entangled states, such as the Bell and GHZ states, are generated from separable states using matrices known to satisfy the Yang-Baxter equation and its generalization. This remarkable fact hints at the possibility of using braiding…
We apply the fusion procedure to a quantum Yang-Baxter algebra associated with time-discrete integrable systems, notably integrable quantum mappings. We present a general construction of higher-order quantum invariants for these systems. As…