1,266 research outputs found
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
Hamilton-Jacobi Theory and Information Geometry
Recently, a method to dynamically define a divergence function for a
given statistical manifold by means of the
Hamilton-Jacobi theory associated with a suitable Lagrangian function
on has been proposed. Here we will review this
construction and lay the basis for an inverse problem where we assume the
divergence function to be known and we look for a Lagrangian function
for which is a complete solution of the associated
Hamilton-Jacobi theory. To apply these ideas to quantum systems, we have to
replace probability distributions with probability amplitudes.Comment: 8 page
Nonlinear force-free and potential field models of active-region and global coronal fields during the Whole Heliospheric Interval
Between 2008/3/24 and 2008/4/2, the three active regions NOAA active regions
10987, 10988 and 10989 were observed daily by the Synoptic Optical Long-term
Investigations of the Sun (SOLIS) Vector Spectro-Magnetograph (VSM) while they
traversed the solar disk. We use these measurements and the nonlinear
force-free magnetic field code XTRAPOL to reconstruct the coronal magnetic
field for each active region and compare model field lines with images from the
Solar Terrestrial RElations Observatory (STEREO) and Hinode X-ray Telescope
(XRT) telescopes. Synoptic maps made from continuous, round-the-clock Global
Oscillations Network Group (GONG) magnetograms provide information on the
global photospheric field and potential-field source-surface models based on
these maps describe the global coronal field during the Whole Heliospheric
Interval (WHI) and its neighboring rotations. Features of the modeled global
field, such as the coronal holes and streamer belt locations, are discussed in
comparison with extreme ultra-violet and coronagraph observations from STEREO.
The global field is found to be far from a minimum, dipolar state. From the
nonlinear models we compute physical quantities for the active regions such as
the photospheric magnetic and electric current fluxes, the free magnetic energy
and the relative helicity for each region each day where observations permit.
The interconnectivity of the three regions is addressed in the context of the
potential-field source-surface model. Using local and global quantities derived
from the models, we briefly discuss the different observed activity levels of
the regions.Comment: Accepted for publication in the Solar Physics Whole Heliospheric
Interval (WHI) topical issue. We had difficulty squeezing this paper into
arXiv's 15 Mb limit. The full paper is available here
ftp://gong2.nso.edu/dsds_user/petrie/PetrieCanouAmari.pd
Information geometry of density matrices and state estimation
Given a pure state vector |x> and a density matrix rho, the function
p(x|rho)= defines a probability density on the space of pure states
parameterised by density matrices. The associated Fisher-Rao information
measure is used to define a unitary invariant Riemannian metric on the space of
density matrices. An alternative derivation of the metric, based on square-root
density matrices and trace norms, is provided. This is applied to the problem
of quantum-state estimation. In the simplest case of unitary parameter
estimation, new higher-order corrections to the uncertainty relations,
applicable to general mixed states, are derived.Comment: published versio
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.Comment: 22 page
The 3D structure of an active region filament as extrapolated from photospheric and chromospheric observations
The 3D structure of an active region (AR) filament is studied using nonlinear
force-free field (NLFFF) extrapolations based on simultaneous observations at a
photospheric and a chromospheric height. To that end, we used the Si I 10827
\AA\ line and the He I 10830 \AA\ triplet obtained with the Tenerife Infrared
Polarimeter (TIP) at the VTT (Tenerife). The two extrapolations have been
carried out independently from each other and their respective spatial domains
overlap in a considerable height range. This opens up new possibilities for
diagnostics in addition to the usual ones obtained through a single
extrapolation from, typically, a photospheric layer. Among those possibilities,
this method allows the determination of an average formation height of the He I
10830 \AA\ signal of \approx 2 Mm above the surface of the sun. It allows, as
well, to cross-check the obtained 3D magnetic structures in view of verifying a
possible deviation from the force- free condition especially at the
photosphere. The extrapolations yield a filament formed by a twisted flux rope
whose axis is located at about 1.4 Mm above the solar surface. The twisted
field lines make slightly more than one turn along the filament within our box,
which results in 0.055 turns/Mm. The convex part of the field lines (as seen
from the solar surface) constitute dips where the plasma can naturally be
supported. The obtained 3D magnetic structure of the filament depends on the
choice of the observed horizontal magnetic field as determined from the
180\circ solution of the azimuth. We derive a method to check for the
correctness of the selected 180\circ ambiguity solution.Comment: 31 pages, 13 figures, ApJ Accepte
Coordinated analysis of two graphite grains from the CO3.0 LAP 031117 meteorite: First identification of a CO Nova graphite and a presolar iron sulfide subgrain
Presolar grains constitute remnants of stars that existed before the formation of the solar system.
In addition to providing direct information on the materials from which the solar system formed, these grains provide ground-truth information for models of stellar evolution and nucleosynthesis.
Here we report the in-situ identification of two unique presolar graphite grains from the primitive meteorite LaPaz Icefield 031117. Based on these two graphite grains, we estimate a bulk presolar graphite abundance of 5-3+7 ppm in this meteorite. One of the grains (LAP-141) is characterized by an enrichment in 12C and depletions in 33,34S, and contains a small iron sulfide subgrain, representing the first unambiguous identification of presolar iron sulfide. The other grain (LAP-149) is extremely 13C-rich and 15N-poor, with one of the lowest 12C/13C ratios observed among presolar grains. Comparison of its isotopic compositions with new stellar
nucleosynthesis and dust condensation models indicates an origin in the ejecta of a low-mass CO nova. Grain LAP-149 is the first putative nova grain that quantitatively best matches nova model
predictions, providing the first strong evidence for graphite condensation in nova ejecta. Our discovery confirms that CO nova graphite and presolar iron sulfide contributed to the original building blocks of the solar system.Peer ReviewedPostprint (author's final draft
Transient dynamics for sequence processing neural networks
An exact solution of the transient dynamics for a sequential associative
memory model is discussed through both the path-integral method and the
statistical neurodynamics. Although the path-integral method has the ability to
give an exact solution of the transient dynamics, only stationary properties
have been discussed for the sequential associative memory. We have succeeded in
deriving an exact macroscopic description of the transient dynamics by
analyzing the correlation of crosstalk noise. Surprisingly, the order parameter
equations of this exact solution are completely equivalent to those of the
statistical neurodynamics, which is an approximation theory that assumes
crosstalk noise to obey the Gaussian distribution. In order to examine our
theoretical findings, we numerically obtain cumulants of the crosstalk noise.
We verify that the third- and fourth-order cumulants are equal to zero, and
that the crosstalk noise is normally distributed even in the non-retrieval
case. We show that the results obtained by our theory agree with those obtained
by computer simulations. We have also found that the macroscopic unstable state
completely coincides with the separatrix.Comment: 21 pages, 4 figure
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