3,124 research outputs found
Lower Bounds on Mutual Information
We correct claims about lower bounds on mutual information (MI) between
real-valued random variables made in A. Kraskov {\it et al.}, Phys. Rev. E {\bf
69}, 066138 (2004). We show that non-trivial lower bounds on MI in terms of
linear correlations depend on the marginal (single variable) distributions.
This is so in spite of the invariance of MI under reparametrizations, because
linear correlations are not invariant under them. The simplest bounds are
obtained for Gaussians, but the most interesting ones for practical purposes
are obtained for uniform marginal distributions. The latter can be enforced in
general by using the ranks of the individual variables instead of their actual
values, in which case one obtains bounds on MI in terms of Spearman correlation
coefficients. We show with gene expression data that these bounds are in
general non-trivial, and the degree of their (non-)saturation yields valuable
insight.Comment: 4 page
Evolving Newton's Constant, Extended Gravity Theories and SnIa Data Analysis
If Newton's constant G evolves on cosmological timescales as predicted by
extended gravity theories then Type Ia supernovae (SnIa) can not be treated as
standard candles. The magnitude-redshift datasets however can still be useful.
They can be used to simultaneously fit for both H(z) and G(z) (so that local
G(z) constraints are also satisfied) in the context of appropriate
parametrizations. Here we demonstrate how can this analysis be done by applying
it to the Gold SnIa dataset. We compare the derived effective equation of state
parameter w(z) at best fit with the corresponding result obtained by neglecting
the evolution G(z). We show that even though the results clearly differ from
each other, in both cases the best fit w(z) crosses the phantom divide w=-1. We
then attempt to reconstruct a scalar tensor theory that predicts the derived
best fit forms of H(z) and G(z). Since the best fit G(z) fixes the scalar
tensor potential evolution F(z), there is no ambiguity in the reconstruction
and the potential U(z) can be derived uniquely. The particular reconstructed
scalar tensor theory however, involves a change of sign of the kinetic term
as in the minimally coupled case.Comment: Minor changes. Accepted in Phys. Rev. D. 7 revtex pages, 5 figures.
The mathematica file with the numerical analysis of the paper is available at
http://leandros.physics.uoi.gr/snevol.ht
Interpreting the High Frequency QPO Power Spectra of Accreting Black Holes
In the context of a relativistic hot spot model, we investigate different
physical mechanisms to explain the behavior of quasi-periodic oscillations
(QPOs) from accreting black holes. The locations and amplitudes of the QPO
peaks are determined by the ray-tracing calculations presented in Schnittman &
Bertschinger (2004a): the black hole mass and angular momentum give the
geodesic coordinate frequencies, while the disk inclination and the hot spot
size, shape, and overbrightness give the amplitudes of the different peaks. In
this paper additional features are added to the existing model to explain the
broadening of the QPO peaks as well as the damping of higher frequency
harmonics in the power spectrum. We present a number of analytic results that
closely agree with more detailed numerical calculations. Four primary pieces
are developed: the addition of multiple hot spots with random phases, a finite
width in the distribution of geodesic orbits, Poisson sampling of the detected
photons, and the scattering of photons from the hot spot through a corona of
hot electrons around the black hole. Finally, the complete model is used to fit
the observed power spectra of both type A and type B QPOs seen in XTE
J1550-564, giving confidence limits on each of the model parameters.Comment: 30 pages, 5 figures, submitted to Ap
Optimal control technique for Many Body Quantum Systems dynamics
We present an efficient strategy for controlling a vast range of
non-integrable quantum many body one-dimensional systems that can be merged
with state-of-the-art tensor network simulation methods like the density Matrix
Renormalization Group. To demonstrate its potential, we employ it to solve a
major issue in current optical-lattice physics with ultra-cold atoms: we show
how to reduce by about two orders of magnitudes the time needed to bring a
superfluid gas into a Mott insulator state, while suppressing defects by more
than one order of magnitude as compared to current experiments [1]. Finally, we
show that the optimal pulse is robust against atom number fluctuations.Comment: 5 pages, 4 figures, published versio
Pulling adsorbed polymers from surfaces with the AFM: stick versus slip, peeling versus gliding
We consider the response of an adsorbed polymer that is pulled by an AFM
within a simple geometric framework. We separately consider the cases of i)
fixed polymer-surface contact point, ii) sticky case where the polymer is
peeled off from the substrate, and iii) slippery case where the polymer glides
over the surface. The resultant behavior depends on the value of the surface
friction coefficient and the adsorption strength. Our resultant force profiles
in principle allow to extract both from non-equilibrium force-spectroscopic
data.Comment: 6 pages, 3 figures; accepted for publication in Europhys. Lett.,
http://www.edpsciences.org/journal/index.cfm?edpsname=ep
Quantum Fluctuations in Josephson Junction Comparators
We have developed a method for calculation of quantum fluctuation effects, in
particular of the uncertainty zone developing at the potential curvature sign
inversion, for a damped harmonic oscillator with arbitrary time dependence of
frequency and for arbitrary temperature, within the Caldeira-Leggett model. The
method has been applied to the calculation of the gray zone width Delta Ix of
Josephson-junction balanced comparators driven by a specially designed
low-impedance RSFQ circuit. The calculated temperature dependence of Delta Ix
in the range 1.5 to 4.2K is in a virtually perfect agreement with experimental
data for Nb-trilayer comparators with critical current densities of 1.0 and 5.5
kA/cm^2, without any fitting parameters.Comment: 4 pages, 4 figures, submitted to Physical Review Letter
Spectral and Dynamical Properties in Classes of Sparse Networks with Mesoscopic Inhomogeneities
We study structure, eigenvalue spectra and diffusion dynamics in a wide class
of networks with subgraphs (modules) at mesoscopic scale. The networks are
grown within the model with three parameters controlling the number of modules,
their internal structure as scale-free and correlated subgraphs, and the
topology of connecting network. Within the exhaustive spectral analysis for
both the adjacency matrix and the normalized Laplacian matrix we identify the
spectral properties which characterize the mesoscopic structure of sparse
cyclic graphs and trees. The minimally connected nodes, clustering, and the
average connectivity affect the central part of the spectrum. The number of
distinct modules leads to an extra peak at the lower part of the Laplacian
spectrum in cyclic graphs. Such a peak does not occur in the case of
topologically distinct tree-subgraphs connected on a tree. Whereas the
associated eigenvectors remain localized on the subgraphs both in trees and
cyclic graphs. We also find a characteristic pattern of periodic localization
along the chains on the tree for the eigenvector components associated with the
largest eigenvalue equal 2 of the Laplacian. We corroborate the results with
simulations of the random walk on several types of networks. Our results for
the distribution of return-time of the walk to the origin (autocorrelator)
agree well with recent analytical solution for trees, and it appear to be
independent on their mesoscopic and global structure. For the cyclic graphs we
find new results with twice larger stretching exponent of the tail of the
distribution, which is virtually independent on the size of cycles. The
modularity and clustering contribute to a power-law decay at short return
times
Infinite qubit rings with maximal nearest neighbor entanglement: the Bethe ansatz solution
We search for translationally invariant states of qubits on a ring that
maximize the nearest neighbor entanglement. This problem was initially studied
by O'Connor and Wootters [Phys. Rev. A {\bf 63}, 052302 (2001)]. We first map
the problem to the search for the ground state of a spin 1/2 Heisenberg XXZ
model. Using the exact Bethe ansatz solution in the limit of an infinite ring,
we prove the correctness of the assumption of O'Connor and Wootters that the
state of maximal entanglement does not have any pair of neighboring spins
``down'' (or, alternatively spins ``up''). For sufficiently small fixed
magnetization, however, the assumption does not hold: we identify the region of
magnetizations for which the states that maximize the nearest neighbor
entanglement necessarily contain pairs of neighboring spins ``down''.Comment: 10 pages, 4 figures; Eq. (45) and Fig. 3 corrected, no qualitative
change in conclusion
Impulsive quantum measurements: restricted path integral versus von Neumann collapse
The relation between the restricted path integral approach to quantum
measurement theory and the commonly accepted von Neumann wavefunction collapse
postulate is presented. It is argued that in the limit of impulsive
measurements the two approaches lead to the same predictions. The example of
repeated impulsive quantum measurements of position performed on a harmonic
oscillator is discussed in detail and the quantum nondemolition strategies are
recovered in both the approaches.Comment: 12 pages, 3 figure
The Statistics of Crumpled Paper
A statistical study of crumpled paper is allowed by a minimal 1D model: a
self-avoiding line bent at sharp angles -- in which resides the elastic energy
-- put in a confining potential. Many independent equilibrium configurations
are generated numerically and their properties are investigated. At small
confinement, the distribution of segment lengths is log-normal in agreement
with previous predictions and experiments. At high confinement, the system
approaches a jammed state with a critical behavior, whereas the length
distribution follows a Gamma law which parameter is predicted as a function of
the number of layers in the system
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