34,171 research outputs found
Spectral analysis of the free orthogonal matrix
We compute the spectral measure of the standard generators of the
Wang algebra . We show in particular that this measure has support
, and that it has no atoms. The computation is
done by using various techniques, involving the general Wang algebra ,
a representation of due to Woronowicz, and several calculations with
orthogonal polynomials.Comment: 22 pages, 4 figure
Mean eigenvalues for simple, simply connected, compact Lie groups
We determine for each of the simple, simply connected, compact and complex
Lie groups SU(n), Spin and that particular region inside the unit
disk in the complex plane which is filled by their mean eigenvalues. We give
analytical parameterizations for the boundary curves of these so-called trace
figures. The area enclosed by a trace figure turns out to be a rational
multiple of in each case. We calculate also the length of the boundary
curve and determine the radius of the largest circle that is contained in a
trace figure. The discrete center of the corresponding compact complex Lie
group shows up prominently in the form of cusp points of the trace figure
placed symmetrically on the unit circle. For the exceptional Lie groups ,
and with trivial center we determine the (negative) lower bound on
their mean eigenvalues lying within the real interval . We find the
rational boundary values -2/7, -3/13 and -1/31 for , and ,
respectively.Comment: 12 pages, 8 figure
Awareness of Tuberculosis
Delay in diagnosis of pulmonary tuberculosis resulted in the death of 2 patients from the disease, a fatal outcome for a further patient whose cause of death was not determined, and led to extensive lung destruction in 2 others. A plea is made for early investigation of patients presenting with symptoms suggestive of pulmonary tuberculosis
Multiplexed Memory-Insensitive Quantum Repeaters
Long-distance quantum communication via distant pairs of entangled quantum
bits (qubits) is the first step towards more secure message transmission and
distributed quantum computing. To date, the most promising proposals require
quantum repeaters to mitigate the exponential decrease in communication rate
due to optical fiber losses. However, these are exquisitely sensitive to the
lifetimes of their memory elements. We propose a multiplexing of quantum nodes
that should enable the construction of quantum networks that are largely
insensitive to the coherence times of the quantum memory elements.Comment: 5 pages, 4 figures. Accepted for publication in PR
General moments of the inverse real Wishart distribution and orthogonal Weingarten functions
Let be a random positive definite symmetric matrix distributed according
to a real Wishart distribution and let be its inverse
matrix. We compute general moments explicitly. To do so, we employ the orthogonal Weingarten
function, which was recently introduced in the study for Haar-distributed
orthogonal matrices. As applications, we give formulas for moments of traces of
a Wishart matrix and its inverse.Comment: 29 pages. The last version differs from the published version, but it
includes Appendi
Structural model optimization using statistical evaluation
The results of research in applying statistical methods to the problem of structural dynamic system identification are presented. The study is in three parts: a review of previous approaches by other researchers, a development of various linear estimators which might find application, and the design and development of a computer program which uses a Bayesian estimator. The method is tried on two models and is successful where the predicted stiffness matrix is a proper model, e.g., a bending beam is represented by a bending model. Difficulties are encountered when the model concept varies. There is also evidence that nonlinearity must be handled properly to speed the convergence
Weak multiplicativity for random quantum channels
It is known that random quantum channels exhibit significant violations of
multiplicativity of maximum output p-norms for any p>1. In this work, we show
that a weaker variant of multiplicativity nevertheless holds for these
channels. For any constant p>1, given a random quantum channel N (i.e. a
channel whose Stinespring representation corresponds to a random subspace S),
we show that with high probability the maximum output p-norm of n copies of N
decays exponentially with n. The proof is based on relaxing the maximum output
infinity-norm of N to the operator norm of the partial transpose of the
projector onto S, then calculating upper bounds on this quantity using ideas
from random matrix theory.Comment: 21 pages; v2: corrections and additional remark
Next-to-leading order QCD calculations with parton showers II: soft singularities
Programs that calculate observables in quantum chromodynamics at
next-to-leading order typically generate events that consist of partons rather
than hadrons -- and just a few partons at that. These programs would be much
more useful if the few partons were turned into parton showers, which could be
given to one of the Monte Carlo event generators to produce hadron showers. In
a previous paper, we have seen how to generate parton showers related to the
final state collinear singularities of the perturbative calculation for the
example of e+ + e- --> 3 jets. This paper discusses the treatment of the soft
singularities.Comment: 26 pages with 5 figures. This version is close to the version to be
publishe
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