2,303 research outputs found
GRB990123: The Case for Saturated Comptonization
The recent simultaneous detection of optical, X-ray and gamma-ray photons
from GRB990123 during the burst provides the first broadband multi-wavelength
characterization of the burst spectrum and evolution. Here we show that a
direct correlation exists between the time-varying gamma-ray spectral shape and
the prompt optical emission. This combined with the unique signatures of the
time-resolved spectra of GRB990123 convincingly supports earlier predictions of
the saturated Comptonization model. Contrary to other suggestions, we find that
the entire continuum from optical to gamma-rays can be generated from a single
source of leptons (electrons and pairs). The optical flux only appears to lag
the gamma-ray flux due to the high initial Thomson depth of the plasma. Once
the plasma has completely thinned out, the late time afterglow behavior of our
model is the same as in standard models based on the Blandford-McKee (1976)
solution.Comment: 10 pages, including 3 figures and 1 table, submitted to The
Astrophysical Journal Letter
A gentle guide to the basics of two projections theory
This paper is a survey of the basics of the theory of two projections. It contains in particular the theorem by Halmos on two orthogonal projections and Roch, Silbermann, Gohberg, and Krupnik\u27s theorem on two idempotents in Banach algebras. These two theorems, which deliver the desired results usually very quickly and comfortably, are missing or wrongly cited in many recent publications on the topic, The paper is intended as a gentle guide to the field. The basic theorems are precisely stated, some of them are accompanied by full proofs, others not, but precise references are given in each case, and many examples illustrate how to work with the theorems. (C) 2009 Elsevier Inc. All rights reserved
Drazin inversion in the von Neumann algebra generated by two orthogonal projections
Criteria for Drazin and Moore-Penrose invertibility of operators in the von Neumann algebra generated by two orthogonal projections are established and explicit representations for the corresponding inverses are given. The results are illustrated by several examples that have recently been considered in the literature. (C) 2009 Elsevier Inc. All rights reserved
Group inversion in certain finite-dimensional algebras generated by two idempotents
Invertibility in Banach algebras generated by two idempotents can be checked with the help of a theorem by Roch, Silbermann, Gohberg, and Krupnik. This theorem cannot be used to study generalized invertibility. The present paper is devoted to group invertibility in two types of finite-dimensional algebras which are generated by two idempotents, algebras generated by two tightly coupled idempotents on the one hand and algebras of dimension at most four on the other. As a side product, the paper gives the classification of all at most four-dimensional algebras which are generated by two idempotents. (c) 2012 Royal Dutch Mathematical Society (KWG). Published by Elsevier B.V. All rights reserved
Numerical Results for Ground States of Mean-Field Spin Glasses at low Connectivities
An extensive list of results for the ground state properties of spin glasses
on random graphs is presented. These results provide a timely benchmark for
currently developing theoretical techniques based on replica symmetry breaking
that are being tested on mean-field models at low connectivity. Comparison with
existing replica results for such models verifies the strength of those
techniques. Yet, we find that spin glasses on fixed-connectivity graphs (Bethe
lattices) exhibit a richer phenomenology than has been anticipated by theory.
Our data prove to be sufficiently accurate to speculate about some exact
results.Comment: 4 pages, RevTex4, 5 ps-figures included, related papers available at
http://www.physics.emory.edu/faculty/boettcher
Sarma phase in relativistic and non-relativistic systems
We investigate the stability of the Sarma phase in two-component fermion
systems in three spatial dimensions. For this purpose we compare
strongly-correlated systems with either relativistic or non-relativistic
dispersion relation: relativistic quarks and mesons at finite isospin density
and spin-imbalanced ultracold Fermi gases. Using a Functional Renormalization
Group approach, we resolve fluctuation effects onto the corresponding phase
diagrams beyond the mean-field approximation. We find that fluctuations induce
a second order phase transition at zero temperature, and thus a Sarma phase, in
the relativistic setup for large isospin chemical potential. This motivates the
investigation of the cold atoms setup with comparable mean-field phase
structure, where the Sarma phase could then be realized in experiment. However,
for the non-relativistic system we find the stability region of the Sarma phase
to be smaller than the one predicted from mean-field theory. It is limited to
the BEC side of the phase diagram, and the unitary Fermi gas does not support a
Sarma phase at zero temperature. Finally, we propose an ultracold quantum gas
with four fermion species that has a good chance to realize a zero-temperature
Sarma phase.Comment: version published in Phys.Lett.B; 10 pages, 5 figure
Reduction of Dilute Ising Spin Glasses
The recently proposed reduction method for diluted spin glasses is
investigated in depth. In particular, the Edwards-Anderson model with \pm J and
Gaussian bond disorder on hyper-cubic lattices in d=2, 3, and 4 is studied for
a range of bond dilutions. The results demonstrate the effectiveness of using
bond dilution to elucidate low-temperature properties of Ising spin glasses,
and provide a starting point to enhance the methods used in reduction. Based on
that, a greedy heuristic call ``Dominant Bond Reduction'' is introduced and
explored.Comment: 10 pages, revtex, final version, find related material at
http://www.physics.emory.edu/faculty/boettcher
Extremal Optimization for Graph Partitioning
Extremal optimization is a new general-purpose method for approximating
solutions to hard optimization problems. We study the method in detail by way
of the NP-hard graph partitioning problem. We discuss the scaling behavior of
extremal optimization, focusing on the convergence of the average run as a
function of runtime and system size. The method has a single free parameter,
which we determine numerically and justify using a simple argument. Our
numerical results demonstrate that on random graphs, extremal optimization
maintains consistent accuracy for increasing system sizes, with an
approximation error decreasing over runtime roughly as a power law t^(-0.4). On
geometrically structured graphs, the scaling of results from the average run
suggests that these are far from optimal, with large fluctuations between
individual trials. But when only the best runs are considered, results
consistent with theoretical arguments are recovered.Comment: 34 pages, RevTex4, 1 table and 20 ps-figures included, related papers
available at http://www.physics.emory.edu/faculty/boettcher
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