38,105 research outputs found
Random quantum channels I: graphical calculus and the Bell state phenomenon
This paper is the first of a series where we study quantum channels from the
random matrix point of view. We develop a graphical tool that allows us to
compute the expected moments of the output of a random quantum channel. As an
application, we study variations of random matrix models introduced by Hayden
\cite{hayden}, and show that their eigenvalues converge almost surely. In
particular we obtain for some models sharp improvements on the value of the
largest eigenvalue, and this is shown in a further work to have new
applications to minimal output entropy inequalities.Comment: Several typos were correcte
The space-time structure of hard scattering processes
Recent studies of exclusive electroproduction of vector mesons at JLab make
it possible for the first time to play with two independent hard scales: the
virtuality Q^2 of the photon, which sets the observation scale, and the
momentum transfer t to the hadronic system, which sets the interaction scale.
They reinforce the description of hard scattering processes in terms of few
effective degrees of freedom relevant to the Jlab-Hermes energy range.Comment: 4 pages; 5 figure
Naive time-reversal odd phenomena in semi-inclusive deep-inelastic scattering from light-cone constituent quark models
We present results for leading-twist azimuthal asymmetries in semi-inclusive
lepton-nucleon deep-inelastic scattering due to naively time-reversal odd
transverse-momentum dependent parton distribution functions from the light-cone
constituent quark model. We carefully discuss the range of applicability of the
model, especially with regard to positivity constraints and evolution effects.
We find good agreement with available experimental data from COMPASS and
HERMES, and present predictions to be tested in forthcoming experiments at
Jefferson Lab.Comment: 10 pages, 7 figures, discussion of evolution effects extended, to
appear in Phys.Rev.
The X(3872) boson: Molecule or charmonium
It has been argued that the mystery boson X(3872) is a molecule state
consisting of primarily D0-D0*bar + D0bar-D*0. In contrast, apparent puzzles
and potential difficulties have been pointed out for the charmonium assignment
of X(3872). We examine several aspects of these alternatives by
semiquantitative methods since quantitatively accurate results are often hard
to reach on them. We find that some of the observed properties of X(3872), in
particualr, the binding and the production rates are incompatible with the
molecule interpretation. Despite puzzles and obstacles, X(3872) may fit more
likely to the excited triplet P_1 charmonium than to the molecule after mixing
of cc-bar with DD*-bar +Dbar-D* is taken into account. One simple experimental
test is pointed out for distinguishing between a charmonium and an
isospin-mixed molecule in the neutral B decay.Comment: A few sentences of comment are added. One minor rewording in the
Introduction. Two trivial typos are correcte
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
Inelastic final-state interaction
The final-state interaction in multichannel decay processes is sytematically
studied with application to B decay in mind. Since the final-state inteaction
is intrinsically interwoven with the decay interaction in this case, no simple
phase theorem like "Watson's theorem" holds for experimentally observed final
states. We first examine in detail the two-channel problem as a toy-model to
clarify the issues and to remedy common mistakes made in earlier literature.
Realistic multichannel problems are too challenging for quantitative analysis.
To cope with mathematical complexity, we introduce a method of approximation
that is applicable to the case where one prominant inelastic channel dominates
over all others. We illustrate this approximation method in the amplitude of
the decay B to pi K fed by the intermediate states of a charmed meson pair.
Even with our approximation we need more accurate information of strong
interactions than we have now. Nonethless we are able to obtain some insight in
the issue and draw useful conclusions on general fearyres on the strong phases.Comment: The published version. One figure correcte
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
Relative distributions of W's and Z's at low transverse momenta
Despite large uncertainties in the and transverse momentum
() distributions for q_T\lsim 10 GeV, the ratio of the distributions
varys little. The uncertainty in the ratio of to distributions is
on the order of a few percent, independent of the details of the
nonperturbative parameterization.Comment: 13 pages in revtex, 5 postscript figures available upon request,
UIOWA-94-0
Moments of a single entry of circular orthogonal ensembles and Weingarten calculus
Consider a symmetric unitary random matrix
from a circular orthogonal ensemble. In this paper, we study moments of a
single entry . For a diagonal entry we give the explicit
values of the moments, and for an off-diagonal entry we give leading
and subleading terms in the asymptotic expansion with respect to a large matrix
size . Our technique is to apply the Weingarten calculus for a
Haar-distributed unitary matrix.Comment: 17 page
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
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