arXiv subjects

S. A. Ali

Publications and source records attributed to S. A. Ali.

At least 19 recordsLinked to original sources

arXiv2014

Local softening of information geometric indicators of chaos in statistical modeling in the presence of quantum-like considerations

In a previous paper (C. Cafaro et al., 2012), we compared an uncorrelated 3D Gaussian statistical model to an uncorrelated 2D Gaussian statistical model obtained from the former model by introducing a constraint that resembles the quantum mechanical canonical minimum uncertainty relation. Analysis was completed by way of the information geometry and the entropic dynamics of each system. This analysis revealed that the chaoticity of the 2D Gaussian statistical model, quantified by means of the Information Geometric Entropy (IGE), is softened or weakened with respect to the chaoticity of the 3D Gaussian statistical model due to the accessibility of more information. In this companion work, we further constrain the system in the context of a correlation constraint among the system's micro-variables and show that the chaoticity is further weakened, but only locally. Finally, the physicality of the constraints is briefly discussed, particularly in the context of quantum entanglement.

nlin.CD↗

arXiv2012

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.

math-ph↗

arXiv2011

On a Differential Geometric Viewpoint of Jaynes' Maxent Method and its Quantum Extension

We present a differential geometric viewpoint of the quantum MaxEnt estimate of a density operator when only incomplete knowledge encoded in the expectation values of a set of quantum observables is available. Finally, the additional possibility of considering some prior bias towards a certain density operator (the prior) is taken into account and the unsolved issues with its quantum relative entropic inference criterion are pointed out.

math-ph↗

arXiv2011

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.

math-ph↗

arXiv2011

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 σ_{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.

math-ph↗

arXiv2010

Reexamination of an Information Geometric Construction of Entropic Indicators of Complexity

Information geometry and inductive inference methods can be used to model dynamical systems in terms of their probabilistic description on curved statistical manifolds. In this article, we present a formal conceptual reexamination of the information geometric construction of entropic indicators of complexity for statistical models. Specifically, we present conceptual advances in the interpretation of the information geometric entropy (IGE), a statistical indicator of temporal complexity (chaoticity) defined on curved statistical manifolds underlying the probabilistic dynamics of physical systems.

math-ph↗

arXiv2010

Interferometer Response to Scalar Gravitational Waves

It was recently suggested that the magnetic component of Gravitational Waves (GWs) is relevant in the evaluation of frequency response functions of gravitational interferometers. In this paper we extend the analysis to the magnetic component of the scalar mode of GWs which arise from scalar-tensor gravity theory. In the low-frequency approximation, the response function of ground-based interferometers is calculated. The angular dependence of the electric and magnetic contributions to the response function is discussed. Finally, for an arbitrary frequency range, the proper distance between two test masses is calculated and its usefulness in the high-frequency limit for space-based interferometers is briefly considered.

gr-qc↗

arXiv2010

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.

math-ph↗

arXiv2009

Analytical Estimate of Atmospheric Newtonian Noise Generated by Acoustic and Turbulent Phenomena in Laser-Interferometric Gravitational Waves Detectors

We present a theoretical estimate of the atmospheric Newtonian noise due to fluctuations of atmospheric mass densities generated by acoustic and turbulent phenomena and we determine the relevance of such noise in the laser-interferometric detection of gravitational waves. First, we consider the gravitational coupling of interferometer test-masses to fluctuations of atmospheric density due to the propagation of sound waves in a semispace occupied by an ideal fluid delimited by an infinitely rigid plane. We present an analytical expression of the spectrum of acceleration fluctuations of the test-masses of the interferometer in terms of the experimentally obtainable spectrum of pressure fluctuations. Second, we consider the gravitational coupling of interferometer test-masses to fluctuations of atmospheric density due to the propagation of sound waves generated in a turbulent Lighthill process. We present an analytical expression - in the Fourier space - of the spectrum of acceleration fluctuations of the test-masses of the interferometer. Finally, we discuss the relevance of these noise sources in the detection of gravitational waves by comparing the estimated spectral densities of Newtonian atmospheric noises considered here to the expected sensitivity curve of the VIRGO detector.

gr-qc↗

arXiv2009

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.

gr-qc↗

arXiv2009

Can magnetic monopoles and massive photons coexist in the framework of the same classical theory?

It is well known that one cannot construct a self-consistent quantum field theory describing the non-relativistic electromagnetic interaction mediated by massive photons between a point-like electric charge and a magnetic monopole. We show that, indeed, this inconsistency arises in the classical theory itself. No semi-classic approximation or limiting procedure for the Dirac constant approaching to zero is used. As a result, the string attached to the monopole emerges as visible also if finite-range electromagnetic interactions are considered in classical framework.

hep-th↗

arXiv2009

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.

gr-qc↗

arXiv2009

An Application of Reversible Entropic Dynamics on Curved Statistical Manifolds

Entropic Dynamics (ED) is a theoretical framework developed to investigate the possibility that laws of physics reflect laws of inference rather than laws of nature. In this work, a RED (Reversible Entropic Dynamics) model is considered. The geometric structure underlying the curved statistical manifold, M is studied. The trajectories of this particular model are hyperbolic curves (geodesics) on M. Finally, some analysis concerning the stability of these geodesics on M is carried out.

physics.class-ph↗

arXiv2008

Geometrodynamics of Information on Curved Statistical Manifolds and its Applications to Chaos

A novel information-geometrodynamical approach to chaotic dynamics (IGAC) on curved statistical manifolds based on Entropic Dynamics (ED) is presented and a new definition of information geometrodynamical entropy (IGE) as a measure of chaoticity is proposed. The general classical formalism is illustrated in a relatively simple example. It is shown that the hyperbolicity of a non-maximally symmetric 6N-dimensional statistical manifold M_{s} underlying an ED Gaussian model describing an arbitrary system of 3N degrees of freedom leads to linear information-geometric entropy growth and to exponential divergence of the Jacobi vector field intensity, quantum and classical features of chaos respectively. An information-geometric analogue of the Zurek-Paz quantum chaos criterion in the classical reversible limit is proposed. This analogy is illustrated applying the IGAC to a set of n-uncoupled three-dimensional anisotropic inverted harmonic oscillators characterized by a Ohmic distributed frequency spectrum.

math-ph↗

arXiv2008

The Spacetime Algebra Approach to Massive Classical Electrodynamics with Magnetic Monopoles

Maxwell's equations with massive photons and magnetic monopoles are formulated using spacetime algebra. It is demonstrated that a single non-homogeneous multi-vectorial equation describes the theory. Two limiting cases are considered and their symmetries highlighted: massless photons with magnetic monopoles and finite photon mass in the absence of monopoles. Finally, it is shown that the EM-duality invariance is a symmetry of the Hamiltonian density (for Minkowskian spacetime) and Lagrangian density (for Euclidean 4-space) that reflects the signature of the respective metric manifold.

math-ph↗

arXiv2008

Can chaotic quantum energy levels statistics be characterized using information geometry and inference methods?

In this paper, we review our novel information geometrodynamical approach to chaos (IGAC) on curved statistical manifolds and we emphasize the usefulness of our information-geometrodynamical entropy (IGE) as an indicator of chaoticity in a simple application. Furthermore, knowing that integrable and chaotic quantum antiferromagnetic Ising chains are characterized by asymptotic logarithmic and linear growths of their operator space entanglement entropies, respectively, we apply our IGAC to present an alternative characterization of such systems. Remarkably, we show that in the former case the IGE exhibits asymptotic logarithmic growth while in the latter case the IGE exhibits asymptotic linear growth. At this stage of its development, IGAC remains an ambitious unifying information-geometric theoretical construct for the study of chaotic dynamics with several unsolved problems. However, based on our recent findings, we believe it could provide an interesting, innovative and potentially powerful way to study and understand the very important and challenging problems of classical and quantum chaos.

math-ph↗

arXiv2007

Nonlinear Realization of the Local Conform-Affine Symmetry Group for Gravity in the Composite Fiber Bundle Formalism

A gauge theory of gravity based on a nonlinear realization (NLR) of the local Conform-Affine (CA) group of symmetry transformations is presented. The coframe fields and gauge connections of the theory are obtained. The tetrads and Lorentz group metric are used to induce a spacetime metric. The inhomogenously transforming (under the Lorentz group) connection coefficients serve as gravitational gauge potentials used to define covariant derivatives accommodating minimal coupling of matter and gauge fields. On the other hand, the tensor valued connection forms serve as auxillary dynamical fields associated with the dilation, special conformal and deformational (shear) degrees of freedom inherent in the bundle manifold. The bundle curvature of the theory is determined. Boundary topological invariants are constructed. They serve as a prototype (source free) gravitational Lagrangian. The Bianchi identities, covariant field equations and gauge currents are obtained.

gr-qc↗

arXiv2007

Jacobi Fields on Statistical Manifolds of Negative Curvature

Two entropic dynamical models are considered. The geometric structure of the statistical manifolds underlying these models is studied. It is found that in both cases, the resulting metric manifolds are negatively curved. Moreover, the geodesics on each manifold are described by hyperbolic trajectories. A detailed analysis based on the Jacobi equation for geodesic spread is used to show that the hyperbolicity of the manifolds leads to chaotic exponential instability. A comparison between the two models leads to a relation among statistical curvature, stability of geodesics and relative entropy-like quantities. Finally, the Jacobi vector field intensity and the entropy-like quantity are suggested as possible indicators of chaoticity in the ED models due to their similarity to the conventional chaos indicators based on the Riemannian geometric approach and the Zurek-Paz criterion of linear entropy growth, respectively.

nlin.CD↗