1,057 research outputs found
Building effective models from sparse but precise data
A common approach in computational science is to use a set of of highly
precise but expensive calculations to parameterize a model that allows less
precise, but more rapid calculations on larger scale systems. Least-squares
fitting on a model that underfits the data is generally used for this purpose.
For arbitrarily precise data free from statistic noise, e.g. ab initio
calculations, we argue that it is more appropriate to begin with a ensemble of
models that overfit the data. Within a Bayesian framework, a most likely model
can be defined that incorporates physical knowledge, provides error estimates
for systems not included in the fit, and reproduces the original data exactly.
We apply this approach to obtain a cluster expansion model for the Ca[Zr,Ti]O3
solid solution.Comment: 10 pages, 3 figures, submitted to Physical Review Letter
James van Allen and his namesake NASA mission
Abstract
In many ways, James A. Van Allen defined and âinventedâ modern space research. His example showed the way for government-university partners to pursue basic research that also served important national and international goals. He was a tireless advocate for space exploration and for the role of space science in the spectrum of national priorities
Supersymmetric and Shape-Invariant Generalization for Nonresonant and Intensity-Dependent Jaynes-Cummings Systems
A class of shape-invariant bound-state problems which represent transition in
a two-level system introduced earlier are generalized to include arbitrary
energy splittings between the two levels as well as intensity-dependent
interactions. We show that the couple-channel Hamiltonians obtained correspond
to the generalizations of the nonresonant and intensity-dependent nonresonant
Jaynes-Cummings Hamiltonians, widely used in quantized theories of laser. In
this general context, we determine the eigenstates, eigenvalues, the time
evolution matrix and the population inversion matrix factor.Comment: A combined version of quant-ph/0005045 and quant-ph/0005046. 24
pages, LATE
Escort mean values and the characterization of power-law-decaying probability densities
Escort mean values (or -moments) constitute useful theoretical tools for
describing basic features of some probability densities such as those which
asymptotically decay like {\it power laws}. They naturally appear in the study
of many complex dynamical systems, particularly those obeying nonextensive
statistical mechanics, a current generalization of the Boltzmann-Gibbs theory.
They recover standard mean values (or moments) for . Here we discuss the
characterization of a (non-negative) probability density by a suitable set of
all its escort mean values together with the set of all associated normalizing
quantities, provided that all of them converge. This opens the door to a
natural extension of the well known characterization, for the instance,
of a distribution in terms of the standard moments, provided that {\it all} of
them have {\it finite} values. This question would be specially relevant in
connection with probability densities having {\it divergent} values for all
nonvanishing standard moments higher than a given one (e.g., probability
densities asymptotically decaying as power-laws), for which the standard
approach is not applicable. The Cauchy-Lorentz distribution, whose second and
higher even order moments diverge, constitutes a simple illustration of the
interest of this investigation. In this context, we also address some
mathematical subtleties with the aim of clarifying some aspects of an
interesting non-linear generalization of the Fourier Transform, namely, the
so-called -Fourier Transform.Comment: 20 pages (2 Appendices have been added
Supersymmetric Jaynes-Cummings model and its exact solutions
The super-algebraic structure of a generalized version of the Jaynes-Cummings
model is investigated. We find that a Z2 graded extension of the so(2,1) Lie
algebra is the underlying symmetry of this model. It is isomorphic to the
four-dimensional super-algebra u(1/1) with two odd and two even elements.
Differential matrix operators are taken as realization of the elements of the
superalgebra to which the model Hamiltonian belongs. Several examples with
various choices of superpotentials are presented. The energy spectrum and
corresponding wavefunctions are obtained analytically.Comment: 12 pages, no figure
What's wrong with this rebuttal?
A recent rebuttal to criticism of Bell's analysis is shown to be defective by
fault of failure to consider all hypothetical conditions input into the
derivation of Bell Inequalitites.Comment: 2 page
Configurational entropy of Wigner crystals
We present a theoretical study of classical Wigner crystals in two- and
three-dimensional isotropic parabolic traps aiming at understanding and
quantifying the configurational uncertainty due to the presence of multiple
stable configurations. Strongly interacting systems of classical charged
particles confined in traps are known to form regular structures. The number of
distinct arrangements grows very rapidly with the number of particles, many of
these arrangements have quite low occurrence probabilities and often the
lowest-energy structure is not the most probable one. We perform numerical
simulations on systems containing up to 100 particles interacting through
Coulomb and Yukawa forces, and show that the total number of metastable
configurations is not a well defined and representative quantity. Instead, we
propose to rely on the configurational entropy as a robust and objective
measure of uncertainty. The configurational entropy can be understood as the
logarithm of the effective number of states; it is insensitive to the presence
of overlooked low-probability states and can be reliably determined even within
a limited time of a simulation or an experiment.Comment: 12 pages, 8 figures. This is an author-created, un-copyedited version
of an article accepted for publication in J. Phys.: Condens. Matter. IOP
Publishing Ltd is not responsible for any errors or omissions in this version
of the manuscript or any version derived from it. The definitive
publisher-authenticated version is available online at
10.1088/0953-8984/23/7/075302.
An entropy-based class assignment detection approach for RDF data
The RDF-style Knowledge Bases usually contain a certain level of noises known as Semantic Web data quality issues. This paper has introduced a new Semantic Web data quality issue called Incorrect Class Assignment problem that shows the incorrect assignment between instances in the instance-level and corresponding classes in an ontology. We have proposed an approach called CAD (Class Assignment Detector) to find the correctness and incorrectness of relationships between instances and classes by analyzing features of classes in an ontology. Initial experiments conducted on a dataset demonstrate the effectiveness of CAD
Entanglement purification of unknown quantum states
A concern has been expressed that ``the Jaynes principle can produce fake
entanglement'' [R. Horodecki et al., Phys. Rev. A {\bf 59}, 1799 (1999)]. In
this paper we discuss the general problem of distilling maximally entangled
states from copies of a bipartite quantum system about which only partial
information is known, for instance in the form of a given expectation value. We
point out that there is indeed a problem with applying the Jaynes principle of
maximum entropy to more than one copy of a system, but the nature of this
problem is classical and was discussed extensively by Jaynes. Under the
additional assumption that the state of the copies of the
quantum system is exchangeable, one can write down a simple general expression
for . We show how to modify two standard entanglement purification
protocols, one-way hashing and recurrence, so that they can be applied to
exchangeable states. We thus give an explicit algorithm for distilling
entanglement from an unknown or partially known quantum state.Comment: 20 pages RevTeX 3.0 + 1 figure (encapsulated Postscript) Submitted to
Physical Review
Consistency of the Shannon entropy in quantum experiments
The consistency of the Shannon entropy, when applied to outcomes of quantum
experiments, is analysed. It is shown that the Shannon entropy is fully
consistent and its properties are never violated in quantum settings, but
attention must be paid to logical and experimental contexts. This last remark
is shown to apply regardless of the quantum or classical nature of the
experiments.Comment: 12 pages, LaTeX2e/REVTeX4. V5: slightly different than the published
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