Equivalence of quantum field theories related by the θ-exact Seiberg-Witten map

The equivalence of the noncommutative U(N) quantum field theories related by the θ-exact Seiberg-Witten maps is, in this paper, proven to all orders in the perturbation theory with respect to the coupling constant. We show that this holds for super Yang-Mills theories with N=0, 1, 2, 4 supersymmetry. A direct check of this equivalence relation is performed by computing the one-loop quantum corrections to the quadratic part of the effective action in the noncommutative U(1) gauge theory with N=0, 1, 2, 4 supersymmetry.

Locally recurrent functions, density topologies and algebraic genericity

We study the algebraic and topological genericity of certain subsets of locally recurrent functions, obtaining (among other results) algebrability and spaceability within these classes.

Locally recurrent functions, density topologies and algebraic genericity

We study the algebraic and topological genericity of certain subsets of locally recurrent functions, obtaining (among other results) algebrability and spaceability within these classes.

Los proverbios de animales en árabe clásico: análisis, estudio comparativo y equivalencias en español

This study entitled «Classical Arabic proverbs: analysis, comparative study and equivalence in Spanish», aims on one hand, to display the multiple problems we face when translating proverbs between Arabic and Spanish, and on the other hand, offers an updated check up of the proverbs uses as well as an analysis of the equivalence between proverbs. It was an arduous task looking for reference works which were of interest to our research both in Arabic and Spanish. We consulted many references but if we were to cite the most important ones, we would talk about works such as Magma alamtal by al-Maydani, which constituted the base we relied on in the analytical part of our work. Also of interest was Hayatu Al-Hayauani l-al-Kubra, from ad-Dummayri and his other work Mungid al-lugati w al-a'lam; as well as Ğamharat al-amtal by Abū Hilāl Al-‘Askarī and Ğamharat al-amtal al-baġdadiyya by‘Abd ar-Rahman Tikritī. As for the references in Spanish, we relied on Martinez Kleiseŕs Ideological General Spanish Proverbs; as well as 1001 Spanish sayings and their correspondence in eight languages from Julia Seville Muñoz and Ortiz de Urbina; also, Introduction to the study of fixed expressions by Julio Casares; Vocabulary of proverbs and proverbial phrases (1627-2000) by G. Correas; Dictionnary of sayings by Campos and Barella; the famous The Ingenious Gentleman Don Quixote of La Mancha by Miguel de Cervantes; the work of Sebastián Orozco de Covarrubias Treasure of Castilian Spanish; as well as Sayings and Proverbs in Romance from Hernán Núñez; or Over 21,000 Castilian Sayings not contained in the Large Collection of the Master Gonzalo Correas by Rodriguez Marín. Our work covered two main levels: a descriptive empirical area that included a historical approach with a definition of the different terms related to the proverbs used in our study. The other level is analytical which, besides holding our personal stamp, has been executed through a rigorous study of the three major aspects of our research: analysis, translation and equivalence of the proverb. We started by making a brief description of the empirical part we have divided into several sections, each devoted to the study of one particular aspect...

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.

Error tolerance of topological codes with independent bit-flip and measurement errors

Topological quantum error correction codes are currently among the most promising candidates for efficiently dealing with the decoherence effects inherently present in quantum devices. Numerically, their theoretical error threshold can be calculated by mapping the underlying quantum problem to a related classical statistical-mechanical spin system with quenched disorder. Here, we present results for the general fault-tolerant regime, where we consider both qubit and measurement errors. However, unlike in previous studies, here we vary the strength of the different error sources independently. Our results highlight peculiar differences between toric and color codes. This study complements previous results published in New J. Phys. 13, 083006 (2011).

Noninvasive imaging of three-dimensional micro and nanostructures by topological methods

We present topological derivative and energy based procedures for the imaging of micro and nano structures using one beam of visible light of a single wavelength. Objects with diameters as small as 10 nm can be located and their position tracked with nanometer precision. Multiple objects dis-tributed either on planes perpendicular to the incidence direction or along axial lines in the incidence direction are distinguishable. More precisely, the shape and size of plane sections perpendicular to the incidence direction can be clearly determined, even for asymmetric and nonconvex scatterers. Axial resolution improves as the size of the objects decreases. Initial reconstructions may proceed by gluing together two-dimensional horizontal slices between axial peaks or by locating objects at three-dimensional peaks of topological energies, depending on the effective wavenumber. Below a threshold size, topological derivative based iterative schemes improve initial predictions of the lo-cation, size, and shape of objects by postprocessing fixed measured data. For larger sizes, tracking the peaks of topological energy fields that average information from additional incident light beams seems to be more effective.