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Showing 1 to 9 of 9 for “"Yang-Baxter equation"”.
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An Examination of the Yang-Baxter Equation
<p>The Yang-Baxter equation has been extensively studied due to its application in numerous fields of mathematics and physics. This thesis sets out to analyze the equation from the viewpoint of the algebraic product of matrices, i.e., the composition of linear maps, with the intent of …
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Quantum Yang-Baxter Equation: Algebraic Constructions and Categorical Perspectives
L'abstract è presente nell'allegato / the abstract is in the attachment
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Deformations of characters, metaplectic Whittaker functions, and the Yang-Baxter equation
… conjecture, which enumerates ASMs, utilized a Yang-Baxter equation for a square ice model from statistical mechanics. In earlier work, Tokuyama and okada gave representation theoretic quantities as generating functions on certain symmetry classes of ASMs or generalizations of them. Brubaker, …
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Integrability from Chern-Simons theories
… 4d Chern-Simons theory and the anti-self-dual Yang-Mills equations. Part one opens with a review of 4d Chern-Simons theory, including a discussion of its connections to both quantum and classical integrable systems. It then turns to the results of this thesis concerning the application of 4d …
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Stochastic Dynamics on Integrable Lattice Models
… six-vertex and dimer model, often related to the Yang–Baxter equation, allow for the construction of associated Markov chains. In some cases, these are measure preserving Markov chains on configurations of the lattice model. In other cases, they arise via transfer matrices, after choosing a …
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Solutions of Matrix Equations
… matrices A and B can make many different matrix equations, e.g., <em>AB</em> = <em>BA</em>, <em>AB</em> = <em>AA</em>, <em>ABA</em> = <em>BAB</em>, and <em>AAB</em> = <em>BAA</em>. It is not always easy to describe solutions to these matrix equations. This thesis considers the problem of …
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Exploring relaxation of magnetization in paramagnetic molecules
… Cu(cryptate) complex using the quantum Yang-Baxter equation (QuYBE) algorithm. We also showed that we can consider response to the external magnetic field via dielectric polarization of pairs of spins and transform the resulting Hamiltonian into that for dimerized XY chain. We argued …
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EXTENDING ACTIONS OF HOPF ALGEBRAS TO ACTIONS OF THE DRINFEL'D DOUBLE
… modules each provide a solution to the quantum Yang-Baxter equation. Solutions of this equation are a source of knot and link invariants and in physics, determine if a one-dimensional quantum system is integrable. Drinfel'd also introduced the Drinfel'd double construction, which produces for …
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Exact Results on Extended Hubbard Models on One-Dimensional Chains
… from the the solutions of a $\mathbb{C}$-number equation (known as Yang-Baxter Equation). In sec.3.3 we first work out a general method of search for solutions of such equation; secondly we explicitly find 96 solutions, corresponding to 96 integrable Extended Hubbard models (most of which are …