38,403 research outputs found
Trace functions as Laplace transforms
We study trace functions on the form t\to\tr f(A+tB) where is a
real function defined on the positive half-line, and and are
matrices such that is positive definite and is positive
semi-definite. If is non-negative and operator monotone decreasing, then
such a trace function can be written as the Laplace transform of a positive
measure. The question is related to the Bessis-Moussa-Villani conjecture.
Key words: Trace functions, BMV-conjecture.Comment: Minor change of style, update of referenc
Inequalities for quantum skew information
We study quantum information inequalities and show that the basic inequality
between the quantum variance and the metric adjusted skew information generates
all the multi-operator matrix inequalities or Robertson type determinant
inequalities studied by a number of authors. We introduce an order relation on
the set of functions representing quantum Fisher information that renders the
set into a lattice with an involution. This order structure generates new
inequalities for the metric adjusted skew informations. In particular, the
Wigner-Yanase skew information is the maximal skew information with respect to
this order structure in the set of Wigner-Yanase-Dyson skew informations.
Key words and phrases: Quantum covariance, metric adjusted skew information,
Robertson-type uncertainty principle, operator monotone function,
Wigner-Yanase-Dyson skew information
Toward the Jamming Threshold of Sphere Packings: Tunneled Crystals
We have discovered a new family of three-dimensional crystal sphere packings
that are strictly jammed (i.e., mechanically stable) and yet possess an
anomalously low density. This family constitutes an uncountably infinite number
of crystal packings that are subpackings of the densest crystal packings and
are characterized by a high concentration of self-avoiding "tunnels" (chains of
vacancies) that permeate the structures. The fundamental geometric
characteristics of these tunneled crystals command interest in their own right
and are described here in some detail. These include the lattice vectors (that
specify the packing configurations), coordination structure, Voronoi cells, and
density fluctuations. The tunneled crystals are not only candidate structures
for achieving the jamming threshold (lowest-density rigid packing), but may
have substantially broader significance for condensed matter physics and
materials science.Comment: 19 pages, 5 figure
Metric adjusted skew information: Convexity and restricted forms of superadditivity
We give a truly elementary proof of the convexity of metric adjusted skew
information following an idea of Effros. We extend earlier results of weak
forms of superadditivity to general metric adjusted skew informations.
Recently, Luo and Zhang introduced the notion of semi-quantum states on a
bipartite system and proved superadditivity of the Wigner-Yanase-Dyson skew
informations for such states. We extend this result to general metric adjusted
skew informations. We finally show that a recently introduced extension to
parameter values of the WYD-information is a special case of
(unbounded) metric adjusted skew information.Comment: An error in the literature is pointed ou
Crossover Behavior in Burst Avalanches of Fiber Bundles: Signature of Imminent Failure
Bundles of many fibers, with statistically distributed thresholds for
breakdown of individual fibers and where the load carried by a bursting fiber
is equally distributed among the surviving members, are considered. During the
breakdown process, avalanches consisting of simultaneous rupture of several
fibers occur, with a distribution D(Delta) of the magnitude Delta of such
avalanches. We show that there is, for certain threshold distributions, a
crossover behavior of D(Delta) between two power laws D(Delta) proportional to
Delta^(-xi), with xi=3/2 or xi=5/2. The latter is known to be the generic
behavior, and we give the condition for which the D(Delta) proportional to
Delta^(-3/2) behavior is seen. This crossover is a signal of imminent
catastrophic failure in the fiber bundle. We find the same crossover behavior
in the fuse model.Comment: 4 pages, 4 figure
Asymmetries in the CMB anisotropy field
We report on the results from two independent but complementary statistical
analyses of the WMAP first-year data, based on the power spectrum and N-point
correlation functions. We focus on large and intermediate scales (larger than
about 3 degrees) and compare the observed data against Monte Carlo ensembles
with WMAP-like properties. In both analyses, we measure the amplitudes of the
large-scale fluctuations on opposing hemispheres and study the ratio of the two
amplitudes. The power-spectrum analysis shows that this ratio for WMAP, as
measured along the axis of maximum asymmetry, is high at the 95%-99% level
(depending on the particular multipole range included). The axis of maximum
asymmetry of the WMAP data is weakly dependent on the multipole range under
consideration but tends to lie close to the ecliptic axis. In the N-point
correlation function analysis we focus on the northern and southern hemispheres
defined in ecliptic coordinates, and we find that the ratio of the large-scale
fluctuation amplitudes is high at the 98%-99% level. Furthermore, the results
are stable with respect to choice of Galactic cut and also with respect to
frequency band. A similar asymmetry is found in the COBE-DMR map, and the axis
of maximum asymmetry is close to the one found in the WMAP data.Comment: 6 pages, 5 figures; version to appear in ApJ, textual improvements,
added reference
Classical Nucleation Theory of the One-Component Plasma
We investigate the crystallization rate of a one-component plasma (OCP) in
the context of classical nucleation theory. From our derivation of the free
energy of an arbitrary distribution of solid clusters embedded in a liquid
phase, we derive the steady-state nucleation rate of an OCP as a function of
the Coulomb coupling parameter. Our result for the rate is in accord with
recent molecular dynamics simulations, but it is greater than that of previous
analytical estimates by many orders of magnitude. Further molecular dynamics
simulations of the nucleation rate of a supercooled liquid OCP for several
values of the coupling parameter would clarify the physics of this process.Comment: 6 pages, 1 figure, accepted by PR
The Jahn-Teller active fluoroperovskites : thermo- and magneto optical correlations as function of the -site
Chromium (II) fluoroperovskites are
strongly correlated Jahn-Teller active materials at low temperatures. In this
paper, we examine the role that the -site ion plays in this family of
fluoroperovskites using both experimental methods (XRD, optical absorption
spectroscopy and magnetic fields) and DFT simulations. Temperature-dependent
optical absorption experiments show that the spin-allowed transitions and
only merge completely for = Na at 2 K. Field-dependent optical
absorption measurements at 2 K show that the oscillating strength of the
spin-allowed transitions in increases with increasing
applied field. Direct magneto-structural correlations which suppress the
spin-flip transitions are observed for below its Ne\'el
temperature. In the spin-flip transitions vanish abruptly below
9 K revealing magneto-optical correlations not linked to crystal structure
changes. This suggests that as the long range ordering is reduced local JT
effects in the individual octahedra take control of the
observed behavior. Our results show clear deviation from the pattern found for
the isoelectronic system. The size of the -site cation
is shown to be central in dictating the physical properties and phase
transitions in , opening up the possibility of varying the
composition to create novel states of matter with tuneable properties
Random Diffusion Model with Structure Corrections
The random diffusion model is a continuum model for a conserved scalar
density field driven by diffusive dynamics where the bare diffusion coefficient
is density dependent. We generalize the model from one with a sharp wavenumber
cutoff to one with a more natural large-wavenumber cutoff. We investigate
whether the features seen previously -- namely a slowing down of the system and
the development of a prepeak in the dynamic structure factor at a wavenumber
below the first structure peak -- survive in this model. A method for
extracting information about a hidden prepeak in experimental data is
presented.Comment: 13 pages, 8 figure
Non-equilibrium dynamics in an interacting nanoparticle system
Non-equilibrium dynamics in an interacting Fe-C nanoparticle sample,
exhibiting a low temperature spin glass like phase, has been studied by low
frequency ac-susceptibility and magnetic relaxation experiments. The
non-equilibrium behavior shows characteristic spin glass features, but some
qualitative differences exist. The nature of these differences is discussed.Comment: 7 pages, 11 figure
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