Information Geometric Modeling of Scattering Induced Quantum Entanglement

We present an information geometric analysis of entanglement generated by an s-wave scattering between two Gaussian wave packets. We conjecture that the pre and post-collisional quantum dynamical scenarios related to an elastic head-on collision are macroscopic manifestations emerging from microscopic statistical structures. We then describe them by uncorrelated and correlated Gaussian statistical models, respectively. This allows us to express the entanglement strength in terms of scattering potential and incident particle energies. Furthermore, we show how the entanglement duration can be related to the scattering potential and incident particle energies. Finally, we discuss the connection between entanglement and complexity of motion.Comment: 7 pages; v2 is better than v

Information geometric complexity of a trivariate Gaussian statistical model

We evaluate the information geometric complexity of entropic motion on low-dimensional Gaussian statistical manifolds in order to quantify how difficult is making macroscopic predictions about a systems in the presence of limited information. Specifically, we observe that the complexity of such entropic inferences not only depends on the amount of available pieces of information but also on the manner in which such pieces are correlated. Finally, we uncover that for certain correlational structures, the impossibility of reaching the most favorable configuration from an entropic inference viewpoint, seems to lead to an information geometric analog of the well-known frustration effect that occurs in statistical physics.Comment: 16 pages, 1 figur

Information geometric methods for complexity

Research on the use of information geometry (IG) in modern physics has witnessed significant advances recently. In this review article, we report on the utilization of IG methods to define measures of complexity in both classical and, whenever available, quantum physical settings. A paradigmatic example of a dramatic change in complexity is given by phase transitions (PTs). Hence we review both global and local aspects of PTs described in terms of the scalar curvature of the parameter manifold and the components of the metric tensor, respectively. We also report on the behavior of geodesic paths on the parameter manifold used to gain insight into the dynamics of PTs. Going further, we survey measures of complexity arising in the geometric framework. In particular, we quantify complexity of networks in terms of the Riemannian volume of the parameter space of a statistical manifold associated with a given network. We are also concerned with complexity measures that account for the interactions of a given number of parts of a system that cannot be described in terms of a smaller number of parts of the system. Finally, we investigate complexity measures of entropic motion on curved statistical manifolds that arise from a probabilistic description of physical systems in the presence of limited information. The Kullback-Leibler divergence, the distance to an exponential family and volumes of curved parameter manifolds, are examples of essential IG notions exploited in our discussion of complexity. We conclude by discussing strengths, limits, and possible future applications of IG methods to the physics of complexity.Comment: review article, 60 pages, no figure

The Effect Of Microscopic Correlations On The Information Geometric Complexity Of Gaussian Statistical Models

We present an analytical computation of the asymptotic temporal behavior of the information geometric complexity (IGC) of finite-dimensional Gaussian statistical manifolds in the presence of microcorrelations (correlations between microvariables). We observe a power law decay of the IGC at a rate determined by the correlation coefficient. It is found that microcorrelations lead to the emergence of an asymptotic information geometric compression of the statistical macrostates explored by the system at a faster rate than that observed in absence of microcorrelations. This finding uncovers an important connection between (micro)-correlations and (macro)-complexity in Gaussian statistical dynamical systems.Comment: 12 pages; article in press, Physica A (2010)

Information Geometry of Quantum Entangled Gaussian Wave-Packets

Describing and understanding the essence of quantum entanglement and its connection to dynamical chaos is of great scientific interest. In this work, using information geometric (IG) techniques, we investigate the effects of micro-correlations on the evolution of maximal probability paths on statistical manifolds induced by systems whose microscopic degrees of freedom are Gaussian distributed. We use the statistical manifolds associated with correlated and non-correlated Gaussians to model the scattering induced quantum entanglement of two spinless, structureless, non-relativistic particles, the latter represented by minimum uncertainty Gaussian wave-packets. Knowing that the degree of entanglement is quantified by the purity P of the system, we express the purity for s-wave scattering in terms of the micro-correlation coefficient r - a quantity that parameterizes the correlated microscopic degrees of freedom of the system; thus establishing a connection between entanglement and micro-correlations. Moreover, the correlation coefficient r is readily expressed in terms of physical quantities involved in the scattering, the precise form of which is obtained via our IG approach. It is found that the entanglement duration can be controlled by the initial momentum p_{o}, momentum spread {\sigma}_{o} and r. Furthermore, we obtain exact expressions for the IG analogue of standard indicators of chaos such as the sectional curvatures, Jacobi field intensities and the Lyapunov exponents. We then present an analytical estimate of the information geometric entropy (IGE); a suitable measure that quantifies the complexity of geodesic paths on curved manifolds. Finally, we present concluding remarks addressing the usefulness of an IG characterization of both entanglement and complexity in quantum physics.Comment: 37 pages, 3 figure

Optimal Scheduling of Multiproduct Pipeline System Using MILP Continuous Approach

Part 5: Planning and Scheduling; International audience; To date, the multiproduct pipeline transportation mode has nationally and internationally considerably evolved thanks to his efficiently and effectively of transporting several products. In this paper, we focus our study on the scheduling of a multiproduct pipeline system that receives a number of petroleum products (fuels) from a single refinery source in order to be distributed to several storage and distribution centers (depots). Mixed Integer Linear Programming (MILP) continuous mathematical approach is presented to solve this problem. The sequence of injected products in the same pipeline should be carefully studied, in order to meet market demands and ensure storage autonomy of the marketable pure products in the fuels depots on the one hand and to minimize the number of interfaces; Birth zone of mixture between two products in contact and in sequential flow, which may hinder the continuous operation of the pipeline system, by the necessity of additional storage capacity for this last mixture, that is in no way marketable and requires special processing operations. This work is applied on a real case of a multiproduct pipeline that feeds the western and southwestern region of Algeria with fuels. The obtained results based on the MILP continuous approach give an optimal scheduling of the multiproduct transport system with a minimized number of interfaces. Document type: Conference objec

Can the current state support mechanisms help the growth of renewable energies in wind markets?

The aim of this paper is to provide evidence on the effectiveness of the current state support mechanism incentive adopted by the Italian government in the wind market. In particular, this paper intends to investigate the effectiveness of the auction mechanism as an incentive tool for renewable sources as required by the transposition of Directive 2009/28/EC. In order to demonstrate the economic and financial feasibility of a typical wind-sector investment, we performed a scenario analysis (Monte Carlo simulation) determining a 52,500 Net Present Value (NPV) by varying the key underlying variables of the investment. The results show that with the mechanism currently in place the percentage of positive leveraged NPV is approximately equal to 70%. Despite the state contribution provided through the “Feed-in tariff” mechanism, the profitability of wind projects is not always successful, and this problem could be amplified by the slowness of the authorization procedures. The article offers prime reflections for scholars and policy makers who have long been committed to promoting sustainable development and important considerations on the introduction of further incentive models

Complexity Characterization in a Probabilistic Approach to Dynamical Systems Through Information Geometry and Inductive Inference

Information geometric techniques and inductive inference methods hold great promise for solving computational problems of interest in classical and quantum physics, especially with regard to complexity characterization of dynamical systems in terms of their probabilistic description on curved statistical manifolds. In this article, we investigate the possibility of describing the macroscopic behavior of complex systems in terms of the underlying statistical structure of their microscopic degrees of freedom by use of statistical inductive inference and information geometry. We review the Maximum Relative Entropy (MrE) formalism and the theoretical structure of the information geometrodynamical approach to chaos (IGAC) on statistical manifolds. Special focus is devoted to the description of the roles played by the sectional curvature, the Jacobi field intensity and the information geometrodynamical entropy (IGE). These quantities serve as powerful information geometric complexity measures of information-constrained dynamics associated with arbitrary chaotic and regular systems defined on the statistical manifold. Finally, the application of such information geometric techniques to several theoretical models are presented.Comment: 29 page

A grid-enabled Web Map server

Today Geographic Information Systems (GIS) provide several tools for studying and analyzing varied human and natural phenomena, therefore GIS and geospatial data has grown so much in both public and private organizations. A Challenge is the integration of these data to get innovative and exhaustive knowledge about topics of interest. In this paper we describe the design of a Web Map Service (WMS) OGC-compliant, through the use of grid computing technology and demonstrate how this approach can improve, w.r.t. security, performance, efficiency and scalability, the integration of geospatial multi-source data. End users, with a single sign-on, securely and transparently, gets maps whose data are distributed on heterogeneous data sources belonging to one o more Virtual Organizations via distributed queries in a grid computing environment