Optimal domain of qq-concave operators and vector measure representation of qq-concave Banach lattices

Given a Banach space valued $q$-concave linear operator $T$ defined on a $\sigma$-order continuous quasi-Banach function space, we provide a description of the optimal domain of $T$ preserving $q$-concavity, that is, the largest $\sigma$-order continuous quasi-Banach function space to which $T$ can be extended as a $q$-concave operator. We show in this way the existence of maximal extensions for $q$-concave operators. As an application, we show a representation theorem for $q$-concave Banach lattices through spaces of integrable functions with respect to a vector measure. This result culminates a series of representation theorems for Banach lattices using vector measures that have been obtained in the last twenty years

Symmetry-protected Topological Phases at Finite Temperature

We have applied the recently developed theory of topological Uhlmann numbers to a representative model of a topological insulator in two dimensions, the Qi-Wu-Zhang model. We have found a stable symmetry-protected topological (SPT) phase under external thermal fluctuations in two-dimensions. A complete phase diagram for this model is computed as a function of temperature and coupling constants in the original Hamiltonian. It shows the appearance of large stable phases of matter with topological properties compatible with thermal fluctuations or external noise and the existence of critical lines separating abruptly trivial phases from topological phases. These novel critical temperatures represent thermal topological phase transitions. The initial part of the paper comprises a self-contained explanation of the Uhlmann geometric phase needed to understand the topological properties that it may acquire when applied to topological insulators and superconductors.Comment: Contribution to the focus issue on "Artificial Graphene". Edited by Maciej Lewenstein, Vittorio Pellegrini, Marco Polini and Mordechai (Moti) Sege

Density Matrix Topological Insulators

Thermal noise can destroy topological insulators (TI). However we demonstrate how TIs can be made stable in dissipative systems. To that aim, we introduce the notion of band Liouvillian as the dissipative counterpart of band Hamiltonian, and show a method to evaluate the topological order of its steady state. This is based on a generalization of the Chern number valid for general mixed states (referred to as density matrix Chern value), which witnesses topological order in a system coupled to external noise. Additionally, we study its relation with the electrical conductivity at finite temperature, which is not a topological property. Nonetheless, the density matrix Chern value represents the part of the conductivity which is topological due to the presence of quantum mixed edge states at finite temperature. To make our formalism concrete, we apply these concepts to the two-dimensional Haldane model in the presence of thermal dissipation, but our results hold for arbitrary dimensions and density matrices.Comment: RevTex4 file, color figures. Close to published versio

El plan de desarrollo y ordenamiento territorial del cantón Cuenca, Azuay

El estado actual de un territorio, en el contexto geográfico, es el resultado de las acciones naturales y antrópicas efectuadas sobre un espacio físico, como consecuencia de acciones humanas y decisiones políticas que afectan al territorio, lo que conlleva a desarrollar un territorio en el sentido de pensar y proyectar acciones planificadas sobre un espacio geográfico (Gómez Orea, 2008). La planificación física espacial se sustenta en instrumentos de ordenación del territorio que a su vez se apoya en otras áreas del conocimiento como la demografía, ecología, geología, hidrología, entre otros; y, en los últimos años se ha incorporado la “geomática” a través de herramientas como las tecnologías de la información geográfica. El ordenamiento territorial tiene como objetivo zonificar y sectorizar el espacio geográfico en función de las necesidades de la población para mejorar la calidad de vida de sus habitantes aprovechando los recursos disponibles en armonía con el ambiente, promoviendo un desarrollo económico sostenible en el tiempo. La geomática, a través de las tecnologías de la información geográfica, permite conocer de un espacio geográfico la distribución espacial de los tipos de cobertura vegetal que permiten distinguir bosques nativos y secundarios, áreas naturales protegidas, superficies destinadas a la agricultura y ganadería, complejos fluviales conformados por ríos y cuerpos de agua, entre otros elementos naturales; localización y distribución espacial de centros poblados y asentamientos humanos; información que se genera o consigue ya sea empleando imágenes de satélite, fotografía aérea, registros cartográficos históricos (información secundaria) o mediante el levantamiento de información primaria a través de mediciones con los sistemas satelitales de navegación global (SSNG). El ordenamiento territorial es un instrumento de planificación que permite una adecuada organización política administrativa de un espacio geográfico, con proyección espacial de las políticas de desarrollo social, económico, ambiental y cultural garantizando un nivel de vida apropiado para la población y la conservación del ambiente (Comisión Ordenamiento Territorial, 1994)

Quantum teleportation via maximum-confidence quantum measurements

We investigate the problem of teleporting unknown qudit states via pure quantum channels with nonmaximal Schmidt rank. This process is mapped to the problem of discriminating among nonorthogonal symmetric states which are linearly dependent and equally likely. It is shown that by applying an optimized maximum-confidence (MC) measurement for accomplishing this task, one reaches the maximum possible teleportation fidelity after a conclusive event in the discrimination process, which in turn occurs with the maximum success probability. In this case, such fidelity depends only on the Schmidt rank of the channel and it is larger than the optimal one achieved, deterministically, by the standard teleportation protocol. Furthermore, we show that there are quantum channels for which it is possible to apply a k-stage sequential MC measurement in the discrimination process such that a conclusive event at any stage leads to a teleportation fidelity above the aforementioned optimal one and, consequently, increases the overall success probability of teleportation with a fidelity above this limit.Comment: 14 pages, 6 figure