Quantum discord and information deficit in spin chains

We examine the behavior of quantum correlations of spin pairs in a finite anisotropic $XY$ spin chain immersed in a transverse magnetic field, through the analysis of the quantum discord and the conventional and quadratic one way-information deficits. We first provide a brief review of these measures, showing that the last ones can be obtained as particular cases of a generalized information deficit based on general entropic forms. All these measures coincide with an entanglement entropy in the case of pure states, but can be non-zero in separable mixed states, vanishing just for classically correlated states. It is then shown that their behavior in the exact ground state of the chain exhibits similar features, deviating significantly from that of the pair entanglement below the critical field. In contrast with entanglement, they reach full range in this region, becoming independent of the pair separation and coupling range in the immediate vicinity of the factorizing field. It is also shown, however, that significant differences between the quantum discord and the information deficits arise in the local minimizing measurement that defines them. Both analytical and numerical results are provided.Comment: 14 pages, 5 figure

Local Rigidity in Sandpile Models

We address the problem of the role of the concept of local rigidity in the family of sandpile systems. We define rigidity as the ratio between the critical energy and the amplitude of the external perturbation and we show, in the framework of the Dynamically Driven Renormalization Group (DDRG), that any finite value of the rigidity in a generalized sandpile model renormalizes to an infinite value at the fixed point, i.e. on a large scale. The fixed point value of the rigidity allows then for a non ambiguous distinction between sandpile-like systems and diffusive systems. Numerical simulations support our analytical results.Comment: to be published in Phys. Rev.

Quantum discord in finite XY chains

We examine the quantum discord between two spins in the exact ground state of finite spin 1/2 arrays with anisotropic XY couplings in a transverse field B. It is shown that in the vicinity of the factorizing field B_s, the discord approaches a common finite non-negligible limit which is independent of the pair separation and the coupling range. An analytic expression of this limit is provided. The discord of a mixture of aligned pairs in two different directions, crucial for the previous results, is analyzed in detail, including the evaluation of coherence effects, relevant in small samples and responsible for a parity splitting at B_s. Exact results for finite chains with first neighbor and full range couplings and their interpretation in terms of such mixtures are provided.Comment: 9 pages, 6 figure

Deconstructing the Low-Vol Anomaly

We study several aspects of the so-called low-vol and low-beta anomalies, some already documented (such as the universality of the effect over different geographical zones), others hitherto not clearly discussed in the literature. Our most significant message is that the low-vol anomaly is the result of two independent effects. One is the striking negative correlation between past realized volatility and dividend yield. Second is the fact that ex-dividend returns themselves are weakly dependent on the volatility level, leading to better risk-adjusted returns for low-vol stocks. This effect is further amplified by compounding. We find that the low-vol strategy is not associated to short term reversals, nor does it qualify as a Risk-Premium strategy, since its overall skewness is slightly positive. For practical purposes, the strong dividend bias and the resulting correlation with other valuation metrics (such as Earnings to Price or Book to Price) does make the low-vol strategies to some extent redundant, at least for equities.Comment: 21 pages, 7 figures, 7 tables -- 1 figure adde

Quantum correlations and least disturbing local measurements

We examine the evaluation of the minimum information loss due to an unread local measurement in mixed states of bipartite systems, for a general entropic form. Such quantity provides a measure of quantum correlations, reducing for pure states to the generalized entanglement entropy, while in the case of mixed states it vanishes just for classically correlated states with respect to the measured system, as the quantum discord. General stationary conditions are provided, together with their explicit form for general two-qubit states. Closed expressions for the minimum information loss as measured by quadratic and cubic entropies are also derived for general states of two-qubit systems. As application, we analyze the case of states with maximally mixed marginals, where a general evaluation is provided, as well as X states and the mixture of two aligned states.Comment: 10 pages, 3 figure

Generalized entropic measures of quantum correlations

We propose a general measure of non-classical correlations for bipartite systems based on generalized entropic functions and majorization properties. Defined as the minimum information loss due to a local measurement, in the case of pure states it reduces to the generalized entanglement entropy, i.e., the generalized entropy of the reduced state. However, in the case of mixed states it can be non-zero in separable states, vanishing just for states diagonal in a general product basis, like the Quantum Discord. Simple quadratic measures of quantum correlations arise as a particular case of the present formalism. The minimum information loss due to a joint local measurement is also discussed. The evaluation of these measures in a few simple relevant cases is as well provided, together with comparison with the corresponding entanglement monotones.Comment: 9 pages, 2 figure

Quantum discord and related measures of quantum correlations in XY chains

We examine the quantum correlations of spin pairs in the ground state of finite XY chains in a transverse field, by evaluating the quantum discord as well as other related entropic measures of quantum correlations. A brief review of the latter, based on generalized entropic forms, is also included. It is shown that parity effects are of crucial importance for describing the behavior of these measures below the critical field. It is also shown that these measures reach full range in the immediate vicinity of the factorizing field, where they become independent of separation and coupling range. Analytical and numerical results for the quantum discord, the geometric discord and other measures in spin chains with nearest neighbor coupling and in fully connected spin arrays are also provided.Comment: accepted in Int. J. Mod. Phys. B, special issue "Classical Vs Quantum correlations in composite systems" edited by L. Amico, S. Bose, V. Korepin and V. Vedra

Anderson Localization in Euclidean Random Matrices

We study spectra and localization properties of Euclidean random matrices. The problem is approximately mapped onto that of a matrix defined on a random graph. We introduce a powerful method to find the density of states and the localization threshold. We solve numerically an exact equation for the probability distribution function of the diagonal element of the the resolvent matrix, with a population dynamics algorithm, and we show how this can be used to find the localization threshold. An application of the method in the context of the Instantaneous Normal Modes of a liquid system is given.Comment: 4 page

Tolerance and autoimmunity: novel therapeutic approaches

La función primaria del sistema inmune es resguardar al individuo de los patógenos potencialmente dañinos que invaden el medio ambiente en el cual nos desarrollamos. Este cuenta con dos grandes ramas, la inmunidad innata y la adaptativa, ambas con la propiedad de diferenciar lo peligroso de aquello inofensivo. Estos procesos se hallan regulados por mecanismos homeostáticos que constituyen la tolerancia inmunológica, a los fines de limitar aquellos procesos prolongados y silenciar los potencialmente autoagresivos. Ante la falla de estos mecanismos de control, surgen las enfermedades autoinmunes. Avances en el conocimiento de la fisiopatología de estas entidades, han abierto un nuevo capítulo en el terreno de la inmunofarmacología. Su prometedor potencial actualmente nos ofrece novedosas herramientas terapéuticas para controlar y atenuar el daño causado por este tipo de respuestas. No obstante, debe continuarse la investigación en el campo de los agentes biológicos, ya que ninguno de ellos se encuentra libre de inconvenientes. Seguramente, futuros hallazgos se concretarán en futuros aciertos. Y los aciertos, en Medicina, equivalen a esperanza.The main function of the immune system is to protect the individual against potentially dangerous pathogens. It comprises innate and adaptive cellular and soluble components, both with the capacity to discriminate between harmful and harmless. These processes are regulated by homeostatic mechanisms that constitute the so-called immunological tolerance, which aims to limit the prolonged action of immune mediators and to silence the generation of potentially autoaggressive components. Failure to silence self-reactive T and B cells results in the generation of autoimmune disease. Recent advances in our knowledge of these pathological entities have opened a new chapter in the pharmacology of the immune system. Its promising potential currently offers new therapeutic agents to control and attenuate pathological tissue damage. Nevertheless, further research regarding these biologic agents is required, since they are not free from inconveniences. It is without question that upcoming findings in this field will instill hope into the quest for the “magic bullet”.Fil: Ciliberti, Esteban. Universidad de Buenos Aires. Facultad de Medicina; ArgentinaFil: Carambia, Leandro. Universidad de Buenos Aires. Facultad de Medicina. Departamento de Ciencias Fisiológicas; ArgentinaFil: Cavallin, Sebastian. Universidad de Buenos Aires. Facultad de Medicina. Departamento de Ciencias Fisiológicas; ArgentinaFil: Cerda, Osvaldo L.. Universidad de Buenos Aires. Facultad de Medicina; ArgentinaFil: Poderoso, Juan J.. Universidad de Buenos Aires. Facultad de Medicina. Hospital de Clínicas General San Martín; ArgentinaFil: Rabinovich, Gabriel Adrián. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto de Biología y Medicina Experimental. Fundación de Instituto de Biología y Medicina Experimental. Instituto de Biología y Medicina Experimental; Argentin