On the Decoupling of the Homogeneous and Inhomogeneous Parts in Inhomogeneous Quantum Groups

We show that, if there exists a realization of a Hopf algebra $H$ in a $H$-module algebra $A$, then one can split their cross-product into the tensor product algebra of $A$ itself with a subalgebra isomorphic to $H$ and commuting with $A$. This result applies in particular to the algebra underlying inhomogeneous quantum groups like the Euclidean ones, which are obtained as cross-products of the quantum Euclidean spaces $R_q^N$ with the quantum groups of rotation $U_qso(N)$ of $R_q^N$, for which it has no classical analog.Comment: Latex file, 27 pages. Final version to appear in J. Phys.

Finite-size scaling and the deconfinement transition in gauge theories

We introduce a new method for determining the critical indices of the deconfinement transition in gauge theories. The method is based on the finite size scaling behavior of the expectation value of simple lattice operators, such as the plaquette. We test the method for the case of SU(3) pure gauge theory in (2+1) dimensions and obtain a precise determination of the critical index $\nu$, in agreement with the prediction of the Svetitsky-Yaffe conjecture.Comment: 6 pages. Several comments and one reference added, results unchange

Unbraiding the braided tensor product

We show that the braided tensor product algebra $A_1\underline{\otimes}A_2$ of two module algebras $A_1, A_2$ of a quasitriangular Hopf algebra $H$ is equal to the ordinary tensor product algebra of $A_1$ with a subalgebra of $A_1\underline{\otimes}A_2$ isomorphic to $A_2$, provided there exists a realization of $H$ within $A_1$. In other words, under this assumption we construct a transformation of generators which `decouples' $A_1, A_2$ (i.e. makes them commuting). We apply the theorem to the braided tensor product algebras of two or more quantum group covariant quantum spaces, deformed Heisenberg algebras and q-deformed fuzzy spheres.Comment: LaTex file, 29 page

Baryon loading and the Weibel instability in gamma-ray bursts

The dynamics of two counter-streaming electron-positron-ion unmagnetized plasma shells with zero net charge is analyzed in the context of magnetic field generation in GRB internal shocks due to the Weibel instability. The effects of large thermal motion of plasma particles, arbitrary mixture of plasma species and space charge effects are taken into account. We show that, although thermal effects slow down the instability, baryon loading leads to a non-negligible growth rate even for large temperatures and different shell velocities, thus guaranteeing the robustness and the occurrence of the Weibel instability for a wide range of scenarios.Comment: 6 pages, 4 figures. Accepted for publication in MNRA

Controlling the charge environment of single quantum dots in a photonic-crystal cavity

We demonstrate that the presence of charge around a semiconductor quantum dot (QD) strongly affects its optical properties and produces non-resonant coupling to the modes of a microcavity. We first show that, besides (multi)exciton lines, a QD generates a spectrally broad emission which efficiently couples to cavity modes. Its temporal dynamics shows that it is related to the Coulomb interaction between the QD (multi)excitons and carriers in the adjacent wetting layer. This mechanism can be suppressed by the application of an electric field, making the QD closer to an ideal two-level system.Comment: 12 pages, 4 figure

Frame formalism for the N-dimensional quantum Euclidean spaces

We sketch our recent application of a non-commutative version of the Cartan `moving-frame' formalism to the quantum Euclidean space $R^N_q$, the space which is covariant under the action of the quantum group $SO_q(N)$. For each of the two covariant differential calculi over $R^N_q$ based on the $R$-matrix formalism, we summarize our construction of a frame, the dual inner derivations, a metric and two torsion-free almost metric compatible covariant derivatives with a vanishing curvature. To obtain these results we have developed a technique which fully exploits the quantum group covariance of $R^N_q$. We first find a frame in the larger algebra \Omega^*(R^N_q) \cocross \uqs. Then we define homomorphisms from R^N_q \cocross U_q^{\pm}{so(N)} to $R^N_q$ which we use to project this frame in $\Omega^*(R^N_q)$.Comment: Latex file, 11 pages. Talks given at the Euroconference ``Non-commutative Geometry and Hopf Algebras in Field Theory and Particle Physics'', Villa Gualino (Torino), Sept. 199

Hydration and anomalous solubility of the Bell-Lavis model as solvent

We address the investigation of the solvation properties of the minimal orientational model for water, originally proposed by Bell and Lavis. The model presents two liquid phases separated by a critical line. The difference between the two phases is the presence of structure in the liquid of lower density, described through orientational order of particles. We have considered the effect of small inert solute on the solvent thermodynamic phases. Solute stabilizes the structure of solvent, by the organization of solvent particles around solute particles, at low temperatures. Thus, even at very high densities, the solution presents clusters of structured water particles surrounding solute inert particles, in a region in which pure solvent would be free of structure. Solute intercalates with solvent, a feature which has been suggested by experimental and atomistic simulation data. Examination of solute solubility has yielded a minimum in that property, which may be associated with the minimum found for noble gases. We have obtained a line of minimum solubility (TmS) across the phase diagram, accompanying the line of maximum in density (TMD). This coincidence is easily explained for non-interacting solute and it is in agreement with earlier results in the literature. We give a simple argument which suggests that interacting solute would dislocate TmS to higher temperatures

Baryonic Regge trajectories with analyticity constraints

A model for baryonic Regge trajectories compatible with the threshold behavior required by unitarity and asymptotic behavior in agreement with analyticity constraints is given in explicit form. Widths and masses of the baryonic resonances on the N and $\Delta$ trajectories are reproduced. The MacDowell symmetry is exploited and an application is given.Comment: 12 pages, 6 figure