Results 121 to 130 of about 16,880 (213)

Integrable discretisations and Yang–Baxter maps for super nonlinear Schrödinger systems

Nuclear Physics B
We construct an integrable Grassmann-extended vertex-bond discrete system, which can be restricted to the Grassmann-extended Adler–Yamilov system of partial difference equations, and we derive a Darboux matrix and a Bäcklund transformation for the latter.
Sotiris Konstantinou-Rizos
doaj   +1 more source

O-operators on associative algebras and associative Yang–Baxter equations [PDF]

, 2012
An O-operator on an associative algebra is a generalization of a Rota–Baxter operator that plays an important role in the Hopf algebra approach of Connes and Kreimer to the renormalization of quantum field theory.
Guo, Li, Ni, Xiang, Bai, Chengming
core  

Algebraic classification of Hietarinta’s solutions of Yang-Baxter equations: invertible 4 × 4 operators

Journal of High Energy Physics
In order to examine the simulation of integrable quantum systems using quantum computers, it is crucial to first classify Yang-Baxter operators. Hietarinta was among the first to classify constant Yang-Baxter solutions for a two-dimensional local Hilbert
Somnath Maity, Vivek Kumar Singh, Pramod Padmanabhan, Vladimir Korepin   +3 more
doaj   +1 more source

On Two Non-Ergodic Reversible Cellular Automata, One Classical, the Other Quantum. [PDF]

Entropy (Basel), 2023
Prosen T.
europepmc   +1 more source

Monomial Solutions to Generalized Yang-Baxter Equations in Low Dimensions [PDF]

, 2016
Unitary solutions to the Yang-Baxter equation are important to quantum information science because they lead to unitary representations of the braid group, which can be used to design quantum logic gates that make up topological quantum circuits.
Nemec, Andrew Schmidt
core  

From the braided to the usual Yang-Baxter relation

, 2001
Quantum monodromy matrices coming from a theory of two coupled (m)KdV equations are modified in order to satisfy the usual Yang-Baxter relation. As a consequence, a general connection between braided and unbraided (usual) Yang-Baxter algebras is derived ...
Rossi, M., Fioravanti, D.
core   +1 more source

On the solutions to the multi-parametric Yang–Baxter equations

, 2014
A unified approach is applied in the consideration of the multi-parametric (colored) Yang–Baxter equations (YBE) and the usual YBE with two-parametric R-matrices, relying on the existence of the arbitrary functions in the general solutions.
Khachatryan, Shahane
core   +1 more source

Lax matrices for Yang-Baxter maps

, 2003
It is shown that for a certain class of Yang-Baxter maps (or set-theoretical solutions to the quantum Yang-Baxter equation) the Lax representation can be derived straight from the map itself.
Alexander P Veselov, Yuri B Suris
core  

On derived-indecomposable solutions of the Yang-Baxter equation

Publicacions Matemàtiques
24 pages.
I. Colazzo, M. Ferrara, M. Trombetti
openaire   +5 more sources

Hagedorn singularity in exact U q su 2 $$ {\mathcal{U}}_{\textrm{q}}\left({\mathfrak{su}}_2\right) $$ S-matrix theories with arbitrary spins

Journal of High Energy Physics
Generalizing the quantum sine-Gordon and sausage models, we construct exact S-matrices for higher spin representations with quantum U q su 2 $$ {\mathcal{U}}_{\textrm{q}}\left({\mathfrak{su}}_2\right) $$ symmetry, which satisfy unitarity, crossing ...
Changrim Ahn, Tommaso Franzini, Francesco Ravanini   +2 more
doaj   +1 more source