Excitations and S-matrix for su(3) spin chain combining 3{3} and ${3^{*}}

The associated Hamiltonian for a su(3) spin chain combining ${3}$ and ${3^{*}}$ representations is calculated. The ansatz equations for this chain are obtained and solved in the thermodynamic limit, and the ground state and excitations are described. Thus, relations between the number of roots and the number of holes in each level have been found . The excited states are characterized by means of these quantum numbers. Finally, the exact S matrix for a state with two holes is found.Comment: 17 pages, plaintex, harvmac (to be published in J. of Phys. A

Kneadings, Symbolic Dynamics and Painting Lorenz Chaos. A Tutorial

A new computational technique based on the symbolic description utilizing kneading invariants is proposed and verified for explorations of dynamical and parametric chaos in a few exemplary systems with the Lorenz attractor. The technique allows for uncovering the stunning complexity and universality of bi-parametric structures and detect their organizing centers - codimension-two T-points and separating saddles in the kneading-based scans of the iconic Lorenz equation from hydrodynamics, a normal model from mathematics, and a laser model from nonlinear optics.Comment: Journal of Bifurcations and Chaos, 201

Integrable su(3) spin chain combining different representations

The general expression for the local matrix $t(\theta)$ of a quantum chain with the site space in any representation of su(3) is obtained. This is made by generalizing $t(\theta)$ from the fundamental representation and imposing the fulfillment of the Yang-Baxter equation. Then, a non-homogeneous spin chain combining different representations of su(3) is solved by developing a method inspired in the nested Bethe ansatz. The solution for the eigenvalues of the trace of the monodromy matrix is given as two coupled Bethe equations. A conjecture about the solution of a chain with the site states in different representations of su(n) is presented. The thermodynamic limit of the ground state is calculated.Comment: PlainTex harvmac, 30 pages, 7 figures, to appear in Journal of Physics

Dynamics in a noncommutative phase space

Dynamics has been generalized to a noncommutative phase space. The noncommuting phase space is taken to be invariant under the quantum group $GL_{q,p}(2)$. The $q$-deformed differential calculus on the phase space is formulated and using this, both the Hamiltonian and Lagrangian forms of dynamics have been constructed. In contrast to earlier forms of $q$-dynamics, our formalism has the advantage of preserving the conventional symmetries such as rotational or Lorentz invariance.Comment: LaTeX-twice, 16 page

Quantum Transition State Theory for proton transfer reactions in enzymes

We consider the role of quantum effects in the transfer of hyrogen-like species in enzyme-catalysed reactions. This study is stimulated by claims that the observed magnitude and temperature dependence of kinetic isotope effects imply that quantum tunneling below the energy barrier associated with the transition state significantly enhances the reaction rate in many enzymes. We use a path integral approach which provides a general framework to understand tunneling in a quantum system which interacts with an environment at non-zero temperature. Here the quantum system is the active site of the enzyme and the environment is the surrounding protein and water. Tunneling well below the barrier only occurs for temperatures less than a temperature $T_0$ which is determined by the curvature of potential energy surface near the top of the barrier. We argue that for most enzymes this temperature is less than room temperature. For physically reasonable parameters quantum transition state theory gives a quantitative description of the temperature dependence and magnitude of kinetic isotope effects for two classes of enzymes which have been claimed to exhibit signatures of quantum tunneling. The only quantum effects are those associated with the transition state, both reflection at the barrier top and tunneling just below the barrier. We establish that the friction due to the environment is weak and only slightly modifies the reaction rate. Furthermore, at room temperature and for typical energy barriers environmental degrees of freedom with frequencies much less than 1000 cm$^{-1}$ do not have a significant effect on quantum corrections to the reaction rate.Comment: Aspects of the article are discussed at condensedconcepts.blogspot.co

Exact Solution of a Electron System Combining Two Different t-J Models

A new strongly correlated electron model is presented. This is formed by two types of sites: one where double occupancy is forbidden, as in the t-J model, and the other where double occupancy is allowed but vacancy is not allowed, as an inverse t-J model. The Hamiltonian shows nearest and next-to-nearest neighbour interactions and it is solved by means of a modified algebraic nested Bethe Ansatz. The number of sites where vacancy is not allowed, may be treated as a new parameter if the model is looked at as a t-J model with impurities. The ground and excited states are described in the thermodynamic limit.Comment: Some corrections and references added. To be published in J. Phys.

Effluents from the copper electrorefining as a secondary source of antimony: Role of mass transfer on the recovery by electrodeposition

The limited availability of antimony has increased the need for exploiting alternative sources to its direct extraction from stibnite deposits. Furthermore, introducing recovery techniques in industries where antimony is released in wastewaters leads to more responsible production routes. In this work, electrodeposition is employed to recover the antimony present in a secondary waste effluent of the copper electrorefining that is highly concentrated in hydrochloric acid. The electrochemical characterization of the system was conducted by voltammetry to identify a range of suitable operating conditions for the potentiostatic and galvanostatic electro-recovery of antimony. In potentiostatic mode, the progress of the secondary electrode reactions of hydrogen and chlorine evolution at potentials more cathodic than −0.38 V vs. Ag/AgCl causes the detachment and redissolution of the deposited antimony. Operating under galvanostatic control, similar effects were observed when the limiting current density is exceeded. Current efficiency and specific energy consumption values above 50 % and below 65 kW·h·kg−1, were achieved below the limiting current density (1.265 mA·cm−2). The operational range where electrodeposition of antimony is accelerated at increasing current densities can be broadened at intensified hydrodynamic conditions and higher concentrations of antimony. The detrimental effect of the hydrogen evolution reaction on the recovery of antimony decreases at high HCl concentrations

Thermodynamical limit of general gl(N) spin chains: vacuum state and densities

We study the vacuum state of spin chains where each site carry an arbitrary representation. We prove that the string hypothesis, usually used to solve the Bethe ansatz equations, is valid for representations characterized by rectangular Young tableaux. In these cases, we obtain the density of the center of the strings for the vacuum. We work out different examples and, in particular, the spin chains with periodic array of impurities.Comment: Latex file, 27 pages, 5 figures (.eps) A more detailed study of the representations allowing string hypothesis has added. A simpler formula for the densities is given. References added and misprint correcte

Characterization of silicon thin overlayers on rutile \ce{TiO2} (110)-(1x1)

Silicon thin films for coverages ($\theta$) between 0.3 and 3 monolayers have been grown on rutile \ce{TiO2}(110)-(1x1) at room temperature and studied by x-ray and ultra-violet photoelectron spectroscopies, Auger electron spectroscopy, and low energy electron diffraction (LEED). A clear evidence of a strong \ce{Si}/\ce{TiO2} interaction consistent with the high affinity of O for Si has been found. The Ti cations on the substrate are reduced, while the Si film is oxidized, yielding \ce{SiO2} and a mixture of silicon suboxides. Neutral Si atoms are observed at a coverage of 3 monolayers. At the interface region we observe the formation of cross-linking Ti-O-Si bonds. The thin Si overlayer strongly attenuates the $(1 \times 1)$ LEED pattern from the substrate. Finally, thermal annealing results in the improvement of the \ce{SiO2} stoichiometry, but the surface order is not recovered. Using ab-initio density functional theory we have obtained optimum geometrical configurations and corresponding density of states for 1/3 \le \theta \le 1$monolayers of Si adsorbed on the$1 \times 1$ two-dimensional unit cell