Pseudoscalar susceptibilities and quark condensates: chiral restoration and lattice screening masses

We derive the formal Ward identities relating pseudoscalar susceptibilities and quark condensates in three-flavor QCD, including consistently the 77-n' sector and the U-A(1) anomaly. These identities are verified in the low-energy realization provided by ChPT, both in the standard SU(3) framework for the octet case and combining the use of the SU(3) framework and the large-Nc expansion of QCD to account properly for the nonet sector and anomalous contributions. The analysis is performed including finite temperature corrections as well as the calculation of U(3) quark condensates and all pseudoscalar susceptibilities, which together with the full set of Ward identities, are new results of this work. Finally, the Ward identities are used to derive scaling relations for pseudoscalar masses which explain the behavior with temperature of lattice screening masses near chiral symmetry restoration.

Quantum simulation of a topological Mott insulator with Rydberg atoms in a Lieb lattice

We propose a realistic scheme to quantum simulate the so-far experimentally unobserved topological Mott insulator phase-an interaction-driven topological insulator-using cold atoms in an optical Lieb lattice. To this end, we study a system of spinless fermions in a Lieb lattice, exhibiting repulsive nearest-and next-to-nearest-neighbor interactions and derive the associated zero-temperature phase diagram within mean-field approximation. In particular, we analyze how the interactions can dynamically generate a charge density wave ordered, a nematic, and a topologically nontrivial quantum anomalous Hall phase. We characterize the topology of the different phases by the Chern number and discuss the possibility of phase coexistence. Based on the identified phases, we propose a realistic implementation of this model using cold Rydberg-dressed atoms in an optical lattice. The scheme, which allows one to access, in particular, the topological Mott insulator phase, robustly and independently of its exact position in parameter space, merely requires global, always-on off-resonant laser coupling to Rydberg states and is feasible with state-of-the-art experimental techniques that have already been demonstrated in the laboratory.

Posproducción de efectos especiales: integración de imagen digital 2D y 3D

Esta investigación aborda el tema de la integración de elementos visuales en 2D y 3D, dentro del entorno de trabajo de posproducción y composición digital para medios audiovisuales, presentando un conjunto de prácticas, ejercicios y metodologías concretas, que permiten comprender el proceso de composición e integración, entre imágenes reales y gráficos generados por ordenador en 3D, así como la importante función que la posproducción desempeña en la producción audiovisual contemporánea.

Multivariate orthogonal polynomials and integrable systems

Multivariate orthogonal polynomials in D real dimensions are considered from the perspective of the Cholesky factorization of a moment matrix. The approach allows for the construction of corresponding multivariate orthogonal polynomials, associated second kind functions, Jacobi type matrices and associated three term relations and also Christoffel-Darboux formulae. The multivariate orthogonal polynomials, their second kind functions and the corresponding Christoffel-Darboux kernels are shown to be quasi-determinants as well as Schur complements of bordered truncations of the moment matrix; quasi-tau functions are introduced. It is proven that the second kind functions are multivariate Cauchy transforms of the multivariate orthogonal polynomials. Discrete and continuous deformations of the measure lead to Toda type integrable hierarchy, being the corresponding flows described through Lax and Zakharov-Shabat equations; bilinear equations are found. Varying size matrix nonlinear partial difference and differential equations of the 2D Toda lattice type are shown to be solved by matrix coefficients of the multivariate orthogonal polynomials. The discrete flows, which are shown to be connected with a Gauss-Borel factorization of the Jacobi type matrices and its quasi-determinants, lead to expressions for the multivariate orthogonal polynomials and their second kind functions in terms of shifted quasi-tau matrices, which generalize to the multidimensional realm, those that relate the Baker and adjoint Baker functions to ratios of Miwa shifted tau-functions in the 1D scenario. In this context, the multivariate extension of the elementary Darboux transformation is given in terms of quasi-determinants of matrices built up by the evaluation, at a poised set of nodes lying in an appropriate hyperplane in R^D, of the multivariate orthogonal polynomials. The multivariate Christoffel formula for the iteration of m elementary Darboux transformations is given as a quasi-determinant. It is shown, using congruences in the space of semi-infinite matrices, that the discrete and continuous flows are intimately connected and determine nonlinear partial difference-differential equations that involve only one site in the integrable lattice behaving as a Kadomstev-Petviashvili type system. Finally, a brief discussion of measures with a particular linear isometry invariance and some of its consequences for the corresponding multivariate polynomials is given. In particular, it is shown that the Toda times that preserve the invariance condition lay in a secant variety of the Veronese variety of the fixed point set of the linear isometry.

A measure of conductivity for lattice fermions at finite density

We study the linear response to an external electric field of a system of fermions in a lattice at zero temperature. This allows to measure numerically the Euclidean conductivity which turns out to be compatible with an analytical calculation for free fermions. The numerical method is generalizable to systems with dynamical interactions where no analytical approach is possible.

Análisis de anomalías gravimétricas y modelación cortical 2D de la región volcánica del Campo de Calatrava (Ciudad Real, España)

La región volcánica de Campo de Calatrava se ha interpretado como un proceso de volcanismo intraplaca desarrollado durante el Neógeno. Se han propuesto dos modelos geodinámicos contrapuestos para explicar el origen de este volcanismo: a) un proceso de rifting en un contexto extensional con un adelgazamiento localizado de corteza; b) un proceso flexural de la litosfera en un contexto compresivo débil sin adelgazamiento de corteza. El análisis de las anomalías gravimétricas de Bouguer y una modelización gravimétrica 2D a escala cortical contribuyen a discriminar entre los modelos geodinámicos propuestos para el origen del volcanismo. Los modelos gravimétricos se han constreñido en base a los estudios sísmicos profundos existentes en la zona y a la cartografía geológica regional. Los modelos gravimétricos descartan un adelgazamiento cortical, lo que cuestiona el modelo de rifting abortado y apoyan la hipótesis alternativa del proceso flexural de la litosfera en régimen compresivo débil como origen del volcanismo bético.