Non-affine geometrization can lead to nonphysical instabilities

Geometrization of dynamics consists of representing trajectories by geodesics on a configuration space with a suitably defined metric. Previously, efforts were made to show that the analysis of dynamical stability can also be carried out within geometrical frameworks, by measuring the broadening rate of a bundle of geodesics. Two known formalisms are via Jacobi and Eisenhart metrics. We find that this geometrical analysis measures the actual stability when the length of any geodesic is proportional to the corresponding time interval. We prove that the Jacobi metric is not always an appropriate parametrization by showing that it predicts chaotic behavior for a system of harmonic oscillators. Furthermore, we show, by explicit calculation, that the correspondence between dynamical- and geometrical-spread is ill-defined for the Jacobi metric. We find that the Eisenhart dynamics corresponds to the actual tangent dynamics and is therefore an appropriate geometrization scheme.Comment: Featured on the Cover of the Journal. 9 pages, 6 figures: http://iopscience.iop.org/1751-8121/48/7/07510

Density of States of Quantum Spin Systems from Isotropic Entanglement

We propose a method which we call "Isotropic Entanglement" (IE), that predicts the eigenvalue distribution of quantum many body (spin) systems (QMBS) with generic interactions. We interpolate between two known approximations by matching fourth moments. Though, such problems can be QMA-complete, our examples show that IE provides an accurate picture of the spectra well beyond what one expects from the first four moments alone. We further show that the interpolation is universal, i.e., independent of the choice of local terms.Comment: 4+ pages, content is as in the published versio

On a Watson-like Uniqueness Theorem and Gevrey Expansions

We present a maximal class of analytic functions, elements of which are in one-to-one correspondence with their asymptotic expansions. In recent decades it has been realized (B. Malgrange, J. Ecalle, J.-P. Ramis, Y. Sibuya et al.), that the formal power series solutions of a wide range of systems of ordinary (even non-linear) analytic differential equations are in fact the Gevrey expansions for the regular solutions. Watson's uniqueness theorem belongs to the foundations of this new theory. This paper contains a discussion of an extension of Watson's uniqueness theorem for classes of functions which admit a Gevrey expansion in angular regions of the complex plane with opening less than or equal to (\frac \pi k,) where (k) is the order of the Gevrey expansion. We present conditions which ensure uniqueness and which suggest an extension of Watson's representation theorem. These results may be applied for solutions of certain classes of differential equations to obtain the best accuracy estimate for the deviation of a solution from a finite sum of the corresponding Gevrey expansion.Comment: 18 pages, 4 figure

Criticality without frustration for quantum spin-1 chains

Frustration-free (FF) spin chains have a property that their ground state minimizes all individual terms in the chain Hamiltonian. We ask how entangled the ground state of a FF quantum spin-s chain with nearest-neighbor interactions can be for small values of s. While FF spin-1/2 chains are known to have unentangled ground states, the case s=1 remains less explored. We propose the first example of a FF translation-invariant spin-1 chain that has a unique highly entangled ground state and exhibits some signatures of a critical behavior. The ground state can be viewed as the uniform superposition of balanced strings of left and right parentheses separated by empty spaces. Entanglement entropy of one half of the chain scales as log(n)/2 + O(1), where n is the number of spins. We prove that the energy gap above the ground state is polynomial in 1/n. The proof relies on a new result concerning statistics of Dyck paths which might be of independent interest.Comment: 11 pages, 2 figures. Version 2: minor changes in the proof of Lemma

Unfrustrated Qudit Chains and their Ground States

We investigate chains of 'd' dimensional quantum spins (qudits) on a line with generic nearest neighbor interactions without translational invariance. We find the conditions under which these systems are not frustrated, i.e. when the ground states are also the common ground states of all the local terms in the Hamiltonians. The states of a quantum spin chain are naturally represented in the Matrix Product States (MPS) framework. Using imaginary time evolution in the MPS ansatz, we numerically investigate the range of parameters in which we expect the ground states to be highly entangled and find them hard to approximate using our MPS method.Comment: 5 pages, 5 figures. Typos correcte

Fabrication And Optical Properties Of Strain-free Self-assembled Mesoscopic Gaas Structures

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)We use a combined process of Ga-assisted deoxidation and local droplet etching to fabricate unstrained mesoscopic GaAs/AlGaAs structures exhibiting a high shape anisotropy with a length up to 1.2 mu m and a width of 150 nm. We demonstrate good controllability over size and morphology of the mesoscopic structures by tuning the growth parameters. Our growth method yields structures, which are coupled to a surrounding quantum well and present unique optical emission features. Microscopic and optical analysis of single structures allows us to demonstrate that single structure emission originates from two different confinement regions, which are spectrally separated and show sharp excitonic lines. Photoluminescence is detected up to room temperature making the structures the ideal candidates for strain-free light emitting/detecting devices.12SisNano (MCTI Brazil)FAPESP [2012/11382-9, 2014/17141-9, 2015/08344-6, 2016/14001-7]CNPq [482729/2013-9, 305769/2015-4, 475343/2013-1]CAPESFundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES

Methodological approaches to the study of cancer risk in the vicinity of pollution sources: the experience of a population-based case–control study of childhood cancer

Background: Environmental exposures are related to the risk of some types of cancer, and children are the most vulnerable group of people. This study seeks to present the methodological approaches used in the papers of our group about risk of childhood cancers in the vicinity of pollution sources (industrial and urban sites). A populationbased case–control study of incident childhood cancers in Spain and their relationship with residential proximity to industrial and urban areas was designed. Two methodological approaches using mixed multiple unconditional logistic regression models to estimate odds ratios (ORs) and 95% confdence intervals (95% CIs) were developed: (a) “near vs. far” analysis, where possible excess risks of cancers in children living near (“near”) versus those living far (“far”) from industrial and urban areas were assessed; and (b) “risk gradient” analysis, where the risk gradient in the vicinity of industries was assessed. For each one of the two approaches, three strategies of analysis were implemented: “joint”, “stratifed”, and “individualized” analysis. Incident cases were obtained from the Spanish Registry of Childhood Cancer (between 1996 and 2011). Results: Applying this methodology, associations between proximity (≤2 km) to specifc industrial and urban zones and risk (OR; 95% CI) of leukemias (1.31; 1.04–1.65 for industrial areas, and 1.28; 1.00–1.53 for urban areas), neuroblastoma (2.12; 1.18–3.83 for both industrial and urban areas), and renal (2.02; 1.16–3.52 for industrial areas) and bone (4.02; 1.73–9.34 for urban areas) tumors have been suggested. Conclusions: The two methodological approaches were used as a very useful and fexible tool to analyze the excess risk of childhood cancers in the vicinity of industrial and urban areas, which can be extrapolated and generalized to other cancers and chronic diseases, and adapted to other types of pollution sources

Error analysis of free probability approximations to the density of states of disordered systems

Theoretical studies of localization, anomalous diffusion and ergodicity breaking require solving the electronic structure of disordered systems. We use free probability to approximate the ensemble- averaged density of states without exact diagonalization. We present an error analysis that quantifies the accuracy using a generalized moment expansion, allowing us to distinguish between different approximations. We identify an approximation that is accurate to the eighth moment across all noise strengths, and contrast this with the perturbation theory and isotropic entanglement theory.Comment: 5 pages, 3 figures, submitted to Phys. Rev. Let

Physical chemical properties and kinetics of redox processes in water/soybean oil microemulsions

Water/oil microemulsions (w/o ME) constituted by water, soybean oil, SDS (sodium dodecyl sulfate) and several short-chain alcohols were characterized from the viewpoint of its physical-chemical and electroanalytical properties. Different co-surfactants and surfactant:co-surfactant ratios were used, and the ME with the most favourable composition was used to study the kinetics of redox processes. For this purpose, cyclic voltammetry measurements using a Pt disk working ultramicroelectrode, an Ag/AgCl reference electrode and a Pt auxiliary electrode, and ferrocene as a probe, were performed. It was verified that the thermodynamic stability of the MEs increases with the co-surfactant content. The molecular structure and water solubility of the co-surfactant affect the electrical conductivity and the hydrodynamic radio of the MEs. Owing to the low diffusion coefficients verified in the MEs, measurements in transient state using conventional sweeping rates could be performed. Ferrocene oxidation in the ME has been demonstrated to proceed in quasi-reversibility conditions. Thus, the possibility of carrying out studies of cyclic voltammetry in vegetable oils under the w/o ME form was demonstrated