Creation and localization of entanglement in a simple configuration of coupled harmonic oscillators

We investigate a simple arrangement of coupled harmonic oscillators which brings out some interesting effects concerning creation of entanglement. It is well known that if each member in a linear chain of coupled harmonic oscillators is prepared in a ``classical state'', such as a pure coherent state or a mixed thermal state, no entanglement is created in the rotating wave approximation. On the other hand, if one of the oscillators is prepared in a nonclassical state (pure squeezed state, for instance), entanglement may be created between members of the chain. In the setup considered here, we found that a great family of nonclassical (squeezed) states can localize entanglement in such a way that distant oscillators never become entangled. We present a detailed study of this particular localization phenomenon. Our results may find application in future solid state implementations of quantum computers, and we suggest an electromechanical system consisting of an array of coupled micromechanical oscillators as a possible implementation.Comment: 7 pages, 8 figures, minor typos fixe

Spectral Triples on Thermodynamic Formalism and Dixmier Trace Representations of Gibbs: theory and examples

In this paper we construct spectral triples $(A,H,D)$ on the symbolic space when the alphabet is finite. We describe some new results for the associated Dixmier trace representations for Gibbs probabilities (for potentials with less regularity than H\"older) and for a certain class of functions. The Dixmier trace representation can be expressed as the limit of a certain zeta function obtained from high order iterations of the Ruelle operator. Among other things we consider a class of examples where we can exhibit the explicit expression for the zeta function. We are also able to apply our reasoning for some parameters of the Dyson model (a potential on the symbolic space $\{-1,1\}^\mathbb{N}$) and for a certain class of observables. Nice results by R. Sharp, M.~Kesseb\"ohmer and T.~Samuel for Dixmier trace representations of Gibbs probabilities considered the case where the potential is of H\"older class. We also analyze a particular case of a pathological continuous potential where the Dixmier trace representation - via the associated zeta function - is not true.Comment: the tile was modified and there are two more author

Evolution of Strigamia centipedes (Chilopoda): a first molecular assessment of phylogeny and divergence times

We present a first phylogenetic and temporal framework, with biogeographical insights, for the centipedes of the genus Strigamia, which are widespread predators in the forest soils of the Northern Hemisphere and comprise the evo-devo model species Strigamia maritima. The phylogeny was estimated by different methods of maximum likelihood and Bayesian inference from sequences of two mitochondrial (16S, COI) and two nuclear (18S, 28S) genes, obtained from 16 species from all major areas of the global range of the genus and encompassing most of the overall morphological and ecological diversity. Divergence times were estimated after calibration upon the fossil record of centipedes. We found that major lineages of extant species of Strigamia separated most probably around 60 million years (Ma) ago. The two most diverse lineages diversified during the last 30 Ma and are today segregated geographically, one in Europe and another in Eastern Asia. This latter region hosts a hitherto underestimated richness and anatomical diversity of species, including three still unknown, yet morphologically well distinct species, which are here described as new: Strigamia inthanoni sp. n. from Thailand, Strigamia korsosi sp. n. from the Ryukyu Islands and Strigamia nana sp. n. from Taiwan. The northern European model species S. maritima is more strictly related to the Eastern Asian lineage, from which it most probably separated around 35 Ma ago before the major diversification of the latter

The effects of tax incentives for small firms on employment levels

This paper will examine the effects of tax incentives for small businesseson employment level evaluating a program with this purpose implemented in Brazil in the 1990s. We first develop a theoretical framework which guides both the de nition of the parameters of interest and their identi cation. Selection problems both into the treatment group and into the data sampleare tackled by combining fi xed effects methods and regression discontinuity design on alternative sub-samples of a longitudinal database of manufacturing fi rms. The results show that on the one hand the size composition of thetreated fi rms may be changed due to the survival of some smaller fi rms that would have exited had it not been eligible to the program. On the other hand, the treated fi rms who do not depend on the program to survive do employ more workers.

Mitochondrial behaviour throughout the lytic cycle of Toxoplasma gondii

Mitochondria distribution in cells controls cellular physiology in health and disease. Here we describe the mitochondrial morphology and positioning found in the different stages of the lytic cycle of the eukaryotic single-cell parasite Toxoplasma gondii. The lytic cycle, driven by the tachyzoite life stage, is responsible for acute toxoplasmosis. It is known that whilst inside a host cell the tachyzoite maintains its single mitochondrion at its periphery. We found that upon parasite transition from the host cell to the extracellular matrix, mitochondrion morphology radically changes, resulting in a reduction in peripheral proximity. This change is reversible upon return to the host, indicating that an active mechanism maintains the peripheral positioning found in the intracellular stages. Comparison between the two states by electron microscopy identified regions of coupling between the mitochondrion outer membrane and the parasite pellicle, whose features suggest the presence of membrane contact sites, and whose abundance changes during the transition between intra- and extra-cellular states. These novel observations pave the way for future research to identify molecular mechanisms involved in mitochondrial distribution in Toxoplasma and the consequences of these mitochondrion changes on parasite physiology

Interior penalty discontinuous Galerkin FEM for the p(x)p(x)-Laplacian

In this paper we construct an "Interior Penalty" Discontinuous Galerkin method to approximate the minimizer of a variational problem related to the $p(x)-$Laplacian. The function $p:\Omega\to [p_1,p_2]$ is log H\"{o}lder continuous and $1<p_1\leq p_2<\infty$. We prove that the minimizers of the discrete functional converge to the solution. We also make some numerical experiments in dimension one to compare this method with the Conforming Galerkin Method, in the case where $p_1$ is close to one. This example is motivated by its applications to image processing.Comment: 26 pages, 2 figure