681 research outputs found
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, Inference Methods and Chaotic Energy Levels Statistics
In this Letter, we propose a novel information-geometric characterization of
chaotic (integrable) energy level statistics of a quantum antiferromagnetic
Ising spin chain in a tilted (transverse) external magnetic field. Finally, we
conjecture our results might find some potential physical applications in
quantum energy level statistics.Comment: 9 pages, added correct journal referenc
On the Poincare Gauge Theory of Gravitation
We present a compact, self-contained review of the conventional gauge
theoretical approach to gravitation based on the local Poincare group of
symmetry transformations. The covariant field equations, Bianchi identities and
conservation laws for angular momentum and energy-momentum are obtained.Comment: v2: minor changes, references added; 18 pages, no figure
Improving the mathematical formulation for the detailed scheduling of refined products pipelines by acconting for flow rate dependent pumping costs
This work presents a continuous-time mixed-integer linear programming (MILP) formulation to find the best detailed schedule for single-source multi-product pipelines, minimizing the total operating costs. By knowing the aggregate plan including pumping and delivery tasks, the best detailed solution tends to minimize pump stoppage/restart costs as well as pumping energy charges associated to the head loss inside the pipeline, which are strongly dependent on the flow rate at every pipeline segment. Pumping costs for transporting products into the pipeline are estimated by introducing a novel piecewise linear calculation of the energy loss. The proposed approach is applied to find the optimal detailed schedule for a real-world case study consisting of a single source pipeline with multiple offtake stations. Important reductions in the operational costs with regards to previous contributions are obtained.Sociedad Argentina de Informática e Investigación Operativ
Abelian Magnetic Monopoles and Topologically Massive Vector Bosons in Scalar-Tensor Gravity with Torsion Potential
A Lagrangian formulation describing the electromagnetic interaction -
mediated by topologically massive vector bosons - between charged, spin-(1/2)
fermions with an abelian magnetic monopole in a curved spacetime with
non-minimal coupling and torsion potential is presented. The covariant field
equations are obtained. The issue of coexistence of massive photons and
magnetic monopoles is addressed in the present framework. It is found that
despite the topological nature of photon mass generation in curved spacetime
with isotropic dilaton field, the classical field theory describing the
nonrelativistic electromagnetic interaction between a point-like electric
charge and magnetic monopole is inconsistent.Comment: 18 pages, no figure
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