New Solutions to the Yang--Baxter Equation from Two--Dimensional Representations of Uq(sl(2))U_q(sl(2)) at Roots of Unit

We present particularly simple new solutions to the Yang--Baxter equation arising from two--dimensional cyclic representations of quantum $SU(2)$. They are readily interpreted as scattering matrices of relativistic objects, and the quantum group becomes a dynamical symmetry.Comment: 11 page

Quantum Groups

These notes correspond rather accurately to the translation of the lectures given at the Fifth Mexican School of Particles and Fields, held in Guanajuato, Gto., in December~1992. They constitute a brief and elementary introduction to quantum symmetries from a physical point of view, along the lines of the forthcoming book by C. G\'omez, G. Sierra and myself.Comment: 37 pages, plain.te

Stretched Horizon for Non-Supersymmetric Black Holes

We review the idea of stretched horizon for extremal black holes in supersymmetric string theories, and we compute it for non-supersymmetric black holes in four dimensions. Only for small masses of the order of the Veneziano wavelength is the stretched horizon bigger than the event horizon.Comment: 4 pages, 2 figures, to appear in the Proceedings of the VIII Mexican School, Oaxaca, AI

Pion Scattering Revisited

Chiral Ward identities lead to consistent accounting for the sigma's width in the linear sigma model's Feynman rules. Reanalysis of pion scattering data at threshold imply a mass for the sigma of 600+ 200 - 100 MeV.Comment: latex; VIII EMPC (Oaxaca, Nov 98) Proceeding

Noise in Grover's Quantum Search Algorithm

Grover's quantum algorithm improves any classical search algorithm. We show how random Gaussian noise at each step of the algorithm can be modelled easily because of the exact recursion formulas available for computing the quantum amplitude in Grover's algorithm. We study the algorithm's intrinsic robustness when no quantum correction codes are used, and evaluate how much noise the algorithm can bear with, in terms of the size of the phone book and a desired probability of finding the correct result. The algorithm loses efficiency when noise is added, but does not slow down. We also study the maximal noise under which the iterated quantum algorithm is just as slow as the classical algorithm. In all cases, the width of the allowed noise scales with the size of the phone book as N^-2/3.Comment: 17 pages, 2 eps figures. Revised version. To be published in PRA, December 199