53,311 research outputs found
Metric adjusted skew information
We extend the concept of Wigner-Yanase-Dyson skew information to something we
call ``metric adjusted skew information'' (of a state with respect to a
conserved observable). This ``skew information'' is intended to be a
non-negative quantity bounded by the variance (of an observable in a state)
that vanishes for observables commuting with the state. We show that the skew
information is a convex function on the manifold of states. It also satisfies
other requirements, proposed by Wigner and Yanase, for an effective
measure-of-information content of a state relative to a conserved observable.
We establish a connection between the geometrical formulation of quantum
statistics as proposed by Chentsov and Morozova and measures of quantum
information as introduced by Wigner and Yanase and extended in this article. We
show that the set of normalized Morozova-Chentsov functions describing the
possible quantum statistics is a Bauer simplex and determine its extreme
points. We determine a particularly simple skew information, the ``lambda-skew
information,'' parametrized by a lambda in (0,1], and show that the convex cone
this family generates coincides with the set of all metric adjusted skew
informations.
Key words: Skew information, convexity, monotone metric, Morozova-Chentsov
function, lambda-skew information.Comment: Edited the abstract and the introductio
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
Viscosity and thermal conductivity of model Jupiter atmospheres
The viscosity and thermal conductivity coefficient are estimated for three models of the atmosphere of Jupiter: a heavy model consisting of 22% helium and 78% hydrogen, a nominal model consisting of 11% helium and 89% hydrogen, and a light model consisting of pure hydrogen. The effect of trace elements is neglected. Linearized approximations are used for the transport coefficients of the mixtures; these are found to be in almost constant ratio to the values for pure hydrogen, independent of temperature. Short Basic language programs for computing the coefficients are listed
Estimating bayesian decision problems with heterogeneous priors
In many areas of economics there is a growing interest in how expertise and
preferences drive individual and group decision making under uncertainty. Increasingly,
we wish to estimate such models to quantify which of these drive decision
making. In this paper we propose a new channel through which we can empirically
identify expertise and preference parameters by using variation in decisions
over heterogeneous priors. Relative to existing estimation approaches, our \PriorBased
Identi cation" extends the possible environments which can be estimated,
and also substantially improves the accuracy and precision of estimates in those
environments which can be estimated using existing methods
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
Dynamic Rearrangements and Packing Regimes in Randomly Deposited Two-Dimensional Granular Beds
We study the structural properties of two-dimensional granular packings
prepared by random deposition from a source line. We consider a class of random
ballistic deposition models based on single-particle relaxation rules
controlled by a critical angle, and we show that these local rules can be
formulated as rolling friction in the framework of dynamic methods for the
simulation of granular materials. We find that a packing prepared by random
deposition models is generically unstable, and undergoes dynamic
rearrangements. As a result, the dynamic method leads systematically to a
higher solid fraction than the geometrical model for the same critical angle.
We characterize the structure of the packings generated by both methods in
terms of solid fraction, contact connectivity and anisotropy. Our analysis
provides evidence for four packing regimes as a function of solid fraction, the
mechanisms of packing growth being different in each regime.Comment: 36 pages, 17 figures to be published in Phys.Rev E. September 200
How many nucleosynthesis processes exist at low metallicity?
Abundances of low-metallicity stars offer a unique opportunity to understand
the contribution and conditions of the different processes that synthesize
heavy elements. Many old, metal-poor stars show a robust abundance pattern for
elements heavier than Ba, and a less robust pattern between Sr and Ag. Here we
probe if two nucleosynthesis processes are sufficient to explain the stellar
abundances at low metallicity, and we carry out a site independent approach to
separate the contribution from these two processes or components to the total
observationally derived abundances. Our approach provides a method to determine
the contribution of each process to the production of elements such as Sr, Zr,
Ba, and Eu. We explore the observed star-to-star abundance scatter as a
function of metallicity that each process leads to. Moreover, we use the
deduced abundance pattern of one of the nucleosynthesis components to constrain
the astrophysical conditions of neutrino-driven winds from core-collapse
supernovae.Comment: 13 pages, published in Ap
Extensions of Lieb's concavity theorem
The operator function (A,B)\to\tr f(A,B)(K^*)K, defined on pairs of bounded
self-adjoint operators in the domain of a function f of two real variables, is
convex for every Hilbert Schmidt operator K, if and only if f is operator
convex. As a special case we obtain a new proof of Lieb's concavity theorem for
the function (A,B)\to\tr A^pK^*B^{q}K, where p and q are non-negative numbers
with sum p+q\le 1. In addition, we prove concavity of the operator function
(A,B)\to \tr(A(A+\mu_1)^{-1}K^* B(B+\mu_2)^{-1}K) on its natural domain
D_2(\mu_1,\mu_2), cf. Definition 4.1Comment: The format of one reference is changed such that CiteBase can
identify i
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