3,153 research outputs found
Component groups of unipotent centralizers in good characteristic
Let G be a connected, reductive group over an algebraically closed field of
good characteristic. For u in G unipotent, we describe the conjugacy classes in
the component group A(u) of the centralizer of u. Our results extend work of
the second author done for simple, adjoint G over the complex numbers.
When G is simple and adjoint, the previous work of the second author makes
our description combinatorial and explicit; moreover, it turns out that
knowledge of the conjugacy classes suffices to determine the group structure of
A(u). Thus we obtain the result, previously known through case-checking, that
the structure of the component group A(u) is independent of good
characteristic.Comment: 13 pages; AMS LaTeX. This is the final version; it will appear in the
Steinberg birthday volume of the Journal of Algebra. This version corrects an
oversight pointed out by the referee; see Prop 2
Medical Bill Problems Steady for U.S. Families, 2007-2010
Examines changes in the proportion of people in families having difficulty paying medical bills during the recession by age group, insurance status, income, amount owed, amount paid off, and estimated time to pay off bills. Considers contributing factors
Modeling cosmic ray anisotropies near 10(18) eV
A galactic magnetic field reversal near the Sagittarius spiral arm may be responsible for the southern excess (or northern shortage) of cosmic rays near 10 to the 18th power eV. The north-south asymmetry produced by such a reversal would increase with energy in the same manner as the observed asymmetry. The existence of a reversal has been inferred from analyses of Faraday rotation measures
Characteristic polynomials in real Ginibre ensembles
We calculate the average of two characteristic polynomials for the real Ginibre ensemble of asymmetric random matrices, and its chiral counterpart. Considered as quadratic forms they determine a skew-symmetric kernel from which all
complex eigenvalue correlations can be derived. Our results are obtained in a very simple fashion without going to an eigenvalue representation, and are completely new in the chiral case. They hold for Gaussian ensembles which are partly symmetric, with kernels given in terms of Hermite and Laguerre polynomials respectively, depending on an asymmetry parameter. This allows us to interpolate between the maximally asymmetric real Ginibre and the Gaussian Orthogonal Ensemble, as well as their chiral counterparts
Statistics of conductance and shot-noise power for chaotic cavities
We report on an analytical study of the statistics of conductance, , and
shot-noise power, , for a chaotic cavity with arbitrary numbers of
channels in two leads and symmetry parameter . With the theory
of Selberg's integral the first four cumulants of and first two cumulants
of are calculated explicitly. We give analytical expressions for the
conductance and shot-noise distributions and determine their exact asymptotics
near the edges up to linear order in distances from the edges. For a
power law for the conductance distribution is exact. All results are also
consistent with numerical simulations.Comment: 7 pages, 3 figures. Proc. of the 3rd Workshop on Quantum Chaos and
Localisation Phenomena, Warsaw, Poland, May 25-27, 200
On the comparison of volumes of quantum states
This paper aims to study the \a-volume of \cK, an arbitrary subset of the
set of density matrices. The \a-volume is a generalization of the
Hilbert-Schmidt volume and the volume induced by partial trace. We obtain
two-side estimates for the \a-volume of \cK in terms of its Hilbert-Schmidt
volume. The analogous estimates between the Bures volume and the \a-volume
are also established. We employ our results to obtain bounds for the
\a-volume of the sets of separable quantum states and of states with positive
partial transpose (PPT). Hence, our asymptotic results provide answers for
questions listed on page 9 in \cite{K. Zyczkowski1998} for large in the
sense of \a-volume.
\vskip 3mm PACS numbers: 02.40.Ft, 03.65.Db, 03.65.Ud, 03.67.M
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