Hopf measuring comonoids and enrichment

We study the existence of universal measuring comonoids $P(A,B)$ for a pair of monoids $A$, $B$ in a braided monoidal closed category, and the associated enrichment of a category of monoids over the monoidal category of comonoids. In symmetric categories, we show that if $A$ is a bimonoid and $B$ is a commutative monoid, then $P(A,B)$ is a bimonoid; in addition, if $A$ is a cocommutative Hopf monoid then $P(A,B)$ always is Hopf. If $A$ is a Hopf monoid, not necessarily cocommutative, then $P(A,B)$ is Hopf if the fundamental theorem of comodules holds; to prove this we give an alternative description of the dualizable $P(A,B)$-comodules and use the theory of Hopf (co)monads. We explore the examples of universal measuring comonoids in vector spaces and graded spaces.Comment: 30 pages. Version 2: re-arrangement of material; expansion of previous section 6, splitting into current sections 6,7,8; fix of graded algebras example, section 11; appendix removed; other minor fixes and edit

Successive minima of toric height functions

Given a toric metrized R-divisor on a toric variety over a global field, we give a formula for the essential minimum of the associated height function. Under suitable positivity conditions, we also give formulae for all the successive minima. We apply these results to the study, in the toric setting, of the relation between the successive minima and other arithmetic invariants like the height and the arithmetic volume. We also apply our formulae to compute the successive minima for several families of examples, including weighted projective spaces, toric bundles and translates of subtori.Comment: To appear in Annales de l'Institut Fourier (Grenoble), 40 pages, 5 figure

Non-perturbative Correlation Effects in Diluted Magnetic Semiconductors

The effects of carrier-impurity correlations due to a Kondo-like spin-spin interaction in diluted magnetic semiconductors are investigated. These correlations are not only responsible for a transfer of spins between the carriers and the impurities, but also produce non-perturbative effects in the spin dynamics such as renormalization of the precession frequency of the carrier spins, which can reach values of several percent in CdMnTe quantum wells. In two-dimensional systems, the precession frequency renormalization for a single electron spin with defined wave vector shows logarithmic divergences similar to those also known from the Kondo problem in metals. For smooth electron distributions, however, the divergences disappear due to the integrability of the logarithm. A possible dephasing mechanism caused by the wave-vector dependence of the electron spin precession frequencies is found to be of minor importance compared to the spin transfer from the carrier to the impurity system. In the Markov limit of the theory, a quasi-equilibrium expression for the carrier-impurity correlation energy can be deduced indicating the formation of strongly correlated carrier-impurity states for temperatures in the mK range

Selective and efficient quantum process tomography in arbitrary finite dimension

The characterization of quantum processes is a key tool in quantum information processing tasks for several reasons: on one hand, it allows one to acknowledge errors in the implementations of quantum algorithms; on the other, it allows one to characterize unknown processes occurring in nature. Bendersky, Pastawski, and Paz [A. Bendersky, F. Pastawski, and J. P. Paz, Phys. Rev. Lett. 100, 190403 (2008)PRLTAO0031-900710.1103/PhysRevLett.100.190403; Phys. Rev. A 80, 032116 (2009)PLRAAN1050-294710.1103/PhysRevA.80.032116] introduced a method to selectively and efficiently measure any given coefficient from the matrix description of a quantum channel. However, this method heavily relies on the construction of maximal sets of mutually unbiased bases (MUBs), which are known to exist only when the dimension of the Hilbert space is the power of a prime number. In this article, we lift the requirement on the dimension by presenting two variations of the method that work on arbitrary finite dimensions: one uses tensor products of maximal sets of MUBs, and the other uses a dimensional cutoff of a higher prime power dimension.Fil: Perito, Ignacio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; ArgentinaFil: Roncaglia, Augusto Jose. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; ArgentinaFil: Bendersky, Ariel Martin. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigación en Ciencias de la Computación. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigación en Ciencias de la Computación; Argentin

Echinoderms diversity in the Southwestern Atlantic

Studies of biodiversity of echinoderms from South America have increased in recent years. Here we summarize sampling done on three expeditions along the Argentinean coast (35º - 55º S) and near the Antarctic Peninsula. The first campaign, Mejillón II (M-II; 2009), was carried out between 35º - 39º S and covered a depth range between 10 to 140 m. The second was part of the Summer Antarctic Campaign 2011 (CAV-III; 2011) that took place around the Antarctic Peninsula, South Shetland and South Orkney Islands (depth range between 67 to 754 m). The last cruise was the final stretch of the Summer Antarctic Campaign 2011 (CAV-IV; 2011), from 39º - 55º S and between 30 - 140 m depth. As result, 74 stations have been studied, of which 68 had at least one echinoderm specimen. From the total number of stations, the occurrence percentages for each class were Asteroidea (68 %), Echinoidea (64 %), Ophiuroidea (55 %), Holothuroidea (51 %) and Crinoidea (20 %). In the M-II campaign, echinoderms were presented in 94 % of the sampled stations, with Echinoidea most frequent (74 %). In the CAV-III campaign echinoderms were presented in all the stations; Ophiuroidea were found in all stations. The lowest occurrence of echinoderms was found in the CAV-IV campaign (82 %), where Asteroidea was present in the 73 % of the samples, and crinoids were absent.Fil: Martinez, Mariano Ignacio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. Museo Argentino de Ciencias Naturales "Bernardino Rivadavia"; ArgentinaFil: Arribas, Lorena Pilar. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. Museo Argentino de Ciencias Naturales "Bernardino Rivadavia"; ArgentinaFil: Berecoechea, Juan José. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. Museo Argentino de Ciencias Naturales "Bernardino Rivadavia"; ArgentinaFil: Brogger, Martin Ignacio. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Nacional Patagónico; ArgentinaFil: Penchaszadeh, Pablo Enrique. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. Museo Argentino de Ciencias Naturales "Bernardino Rivadavia"; Argentin

A geometrical view of scalar modulation instability in optical fibers

Full models of scalar modulation instability (MI) in optical fibers available in the literature usually involve complex formulations. In this paper, we present a novel approach to the analysis of MI in optical fibers by means of a simple geometrical description in the power vs. frequency plane. This formulation allows to relate the shape of the MI gain to any arbitrary dispersion profile of the medium, thus providing a simple insight. As a result, we derive a straightforward explanation of the non-trivial dependence of the cutoff power on high-order dispersion and derive explicitly the power that maximizes the gain. Our approach puts forth a tool to synthesize a desired MI gain with the potential application to a number of parametric-amplification and supercontinuum-generation devices whose initial-stage dynamics rely upon modulation instability.Fil: Hernandez, Santiago Martin. Comisión Nacional de Energía Atómica. Gerencia del Área de Energía Nuclear. Instituto Balseiro; ArgentinaFil: Fierens, Pablo Ignacio. Instituto Tecnológico de Buenos Aires; ArgentinaFil: Bonetti, Juan Ignacio. Comisión Nacional de Energía Atómica. Gerencia del Área de Energía Nuclear. Instituto Balseiro; ArgentinaFil: Sánchez, Alfredo Daniel. Comisión Nacional de Energía Atómica. Gerencia del Área de Energía Nuclear. Instituto Balseiro; ArgentinaFil: Grosz, Diego Fernando. Comisión Nacional de Energía Atómica. Gerencia del Área de Energía Nuclear. Instituto Balseiro; Argentina. Instituto Tecnológico de Buenos Aires; Argentin