OTOC, complexity and entropy in bi-partite systems

There is a remarkable interest in the study of Out-of-time ordered correlators (OTOCs) that goes from many body theory and high energy physics to quantum chaos. In this latter case there is a special focus on the comparison with the traditional measures of quantum complexity such as the spectral statistics, for example. The exponential growth has been verified for many paradigmatic maps and systems. But less is known for multi-partite cases. On the other hand the recently introduced Wigner separability entropy (WSE) and its classical counterpart (CSE) provide with a complexity measure that treats equally quantum and classical distributions in phase space. We have compared the behavior of these measures in a system consisting of two coupled and perturbed cat maps with different dynamics: double hyperbolic (HH), double elliptic (EE) and mixed (HE). In all cases, we have found that the OTOCs and the WSE have essentially the same behavior, providing with a complete characterization in generic bi-partite systems and at the same time revealing them as very good measures of quantum complexity for phase space distributions. Moreover, we establish a relation between both quantities by means of a recently proven theorem linking the second Renyi entropy and OTOCs.Comment: 6 pages, 5 figure

Nonmonotonic Evolution of the Blocking Temperature in Dispersions of Superparamagnetic Nanoparticles

We use a Monte Carlo approach to simulate the influence of the dipolar interaction on assemblies of monodisperse superparamagnetic ${\gamma}-Fe_{2}O_{3}$ nanoparticles. We have identified a critical concentration c*, that marks the transition between two different regimes in the evolution of the blocking temperature ($T_{B}$) with interparticle interactions. At low concentrations (c < c*) magnetic particles behave as an ideal non-interacting system with a constant $T_{B}$. At concentrations c > c* the dipolar energy enhances the anisotropic energy barrier and $T_{B}$ increases with increasing c, so that a larger temperature is required to reach the superparamagnetic state. The fitting of our results with classical particle models and experiments supports the existence of two differentiated regimes. Our data could help to understand apparently contradictory results from the literature.Comment: 13 pages, 7 figure

Homopolar bond formation in ZnV2_2O4_4 close to a metal-insulator transition

Electronic structure calculations for spinel vanadate ZnV$_2$O$_4$ show that partial electronic delocalization in this system leads to structural instabilities. These are a consequence of the proximity to the itinerant-electron boundary, not being related to orbital ordering. We discuss how this mechanism naturally couples charge and lattice degrees of freedom in magnetic insulators close to such a crossover. For the case of ZnV$_2$O$_4$, this leads to the formation of V-V dimers along the [011] and [101] directions that readily accounts for the intriguing magnetic structure of ZnV$_2$O$_4$.Comment: 5 pages, 3 figures, 1 tabl

Competencias de maestros en formación para el análisis epistémico de tareas de razonamiento algebraico elemental

En este trabajo se reportan los resultados de una investigación realizada con un grupo de 28 maestros en formación sobre la manifestación de dos competencias específicas para la formación didáctica de los futuros maestros. La primera se refiere a la selección de ejercicios matemáticos pertinentes para el desarrollo del razonamiento algebraico elemental; la segunda se refiere al conocimiento didáctico específico que favorece el reconocimiento de conceptos, procedimientos y propiedades con fines instruccionales. Se dan algunas implicaciones para la formación de maestros

Razonamiento algebraico en educación primaria: un desafío para la formación de maestros

En este trabajo informamos sobre resultados de un estudio descriptivo-interpretativo sobre el análisis epistémico realizado por un grupo de maestros en formación inicial, de educación primaria, cuando proponen, resuelven y discuten tareas matemáticas que presentan rasgos algebraicos. Se exhibe una tarea matemática propuesta por los estudiantes así como el análisis epistémico respectivo. Se ofrecen algunas implicaciones para la formación inicial de maestros de escuela primaria

Long-term impact of sewage sludge application on soil microbial biomass: An evaluation using meta-analysis

The Long-Term Sludge Experiments (LTSE) began in 1994 as part of continuing research into the effects of sludge-borne heavy metals on soil fertility. The long-term effects of Zn, Cu, and Cd on soil microbial biomass carbon (Cmic) were monitored for 8 years (1997-2005) in sludge amended soils at nine UK field sites. To assess the statutory limits set by the UK Sludge (Use in Agriculture) Regulations the experimental data has been reviewed using the statistical methods of meta-analysis. Previous LTSE studies have focused predominantly on statistical significance rather than effect size, whereas meta-analysis focuses on the magnitude and direction of an effect, i.e. the practical significance, rather than its statistical significance. The results presented here show that significant decreases in Cmic have occurred in soils where the total concentrations of Zn and Cu fall below the current UK statutory limits. For soils receiving sewage sludge predominantly contaminated with Zn, decreases of approximately 7–11% were observed at concentrations below the UK statutory limit. The effect of Zn appeared to increase over time, with increasingly greater decreases in Cmic observed over a period of 8 years. This may be due to an interactive effect between Zn and confounding Cu contamination which has augmented the bioavailability of these metals over time. Similar decreases (7–12%) in Cmic were observed in soils receiving sewage sludge predominantly contaminated with Cu; however, Cmic appeared to show of recovery after a period of 6 years. Application of sewage sludge predominantly contaminated with Cd appeared to have no effect on Cmic at concentrations below the current UK statutory limit

Reflexión sobre conocimientos didácticos-matemáticos emergentes de tareas formativas

Incluir el razonamiento algebraico en la escuela primaria, así como reconocer y tratar las dificultades sobre la concepción de número y su distinción de las formas de representación, requiere de una formación específica en los profesores para que puedan reconocer estos aspectos y promover una enseñanza efectiva en la escuela. El propósito de este taller fue poner en debate conocimientos específicos para la enseñanza de la matemática en la formación de futuros profesores. El diseño de las tareas, su implementación e interpretación fue apoyado en las categorías de análisis de los conocimientos didáctico – matemáticos propuestas por el Enfoque Ontosemiótico del conocimiento y la instrucción matemáticos. El tipo de problemas presentados y la gestión llevada a cabo, generó en los presentes un debate en el que se discutieron aspectos epistémicos, cognitivos, didácticos del conocimiento matemático emergente, y conflictos de significado asociados a ellos. Este trabajo puso en evidencia su potencialidad en el desarrollo de competencias para el análisis didáctico-matemático

Relevant OTOC operators: footprints of the classical dynamics

The out-of-time order correlator (OTOC) has recently become relevant in different areas where it has been linked to scrambling of quantum information and entanglement. It has also been proposed as a good indicator of quantum complexity. In this sense, the OTOC-RE theorem relates the OTOCs summed over a complete base of operators to the second Renyi entropy. Here we have studied the OTOC-RE correspondence on physically meaningful bases like the ones constructed with the Pauli, reflection, and translation operators. The evolution is given by a paradigmatic bi-partite system consisting of two perturbed and coupled Arnold cat maps with different dynamics. We show that the sum over a small set of relevant operators, is enough in order to obtain a very good approximation for the entropy and hence to reveal the character of the dynamics, up to a time t 0 . In turn, this provides with an alternative natural indicator of complexity, i.e. the scaling of the number of relevant operators with time. When represented in phase space, each one of these sets reveals the classical dynamical footprints with different depth according to the chosen base.Comment: 8 pages, 10 figure

Generalized Limits for Parameter Sensitivity via Quantum Ziv-Zakai Bound

We study the generalized limit for parameter sensitivity in quantum estimation theory considering the effects of repeated and adaptive measurements. Based on the quantum Ziv-Zakai bound, we derive some lower bounds for parameter sensitivity when the Hamiltonian of system is unbounded and when the adaptive measurements are implemented on the system. We also prove that the parameter sensitivity is bounded by the limit of the minimum detectable parameter. In particular, we examine several known states in quantum phase estimation with non-interacting photons, and show that they can not perform better than Heisenberg limit in a much simpler way with our result.Comment: 8pages, 5 figure