578 research outputs found
Some minimization problems for the free analogue of the Fisher information
We consider the free non-commutative analogue Phi^*, introduced by D.
Voiculescu, of the concept of Fisher information for random variables. We
determine the minimal possible value of Phi^*(a,a^*), if a is a non-commutative
random variable subject to the constraint that the distribution of aa^* is
prescribed. More generally, we obtain the minimal possible value of
Phi^*({a_{ij},a_{ij}^*), if {a_{ij}} is a family of non-commutative random
variables such that the distribution of AA^* is prescribed, where A is the
matrix (a_{ij}). The d*d-generalization is obtained from the case d=1 via a
result of independent interest, concerning the minimal value of
Phi^*({a_{ij},a_{ij}^*), when the matrix A=(a_{ij}) and its adjoint have a
given joint distribution. We then show how the minimization results obtained
for Phi^* lead to maximization results concerning the free entropy chi^*, also
defined by Voiculescu.Comment: 31 pages, Late
Measurement of the half-life of 198Au in a non-metal: High-precision measurement shows no host-material dependence
We have measured the half-life of the beta decay of 198Au to be 2.6948(9) d,
with the nuclide sited in an insulating environment. Comparing this result with
the half-life we measured previously with a metallic environment, we find the
half-lives in both environments to be the same within 0.04%, thus contradicting
a prediction that screening from a "plasma" of quasi-free electrons in a metal
increases the half-life by as much as 7%
Complete diagrammatics of the single ring theorem
Using diagrammatic techniques, we provide explicit functional relations
between the cumulant generating functions for the biunitarily invariant
ensembles in the limit of large size of matrices. The formalism allows to map
two distinct areas of free random variables: Hermitian positive definite
operators and non-normal R-diagonal operators. We also rederive the
Haagerup-Larsen theorem and show how its recent extension to the eigenvector
correlation function appears naturally within this approach.Comment: 18 pages, 6 figures, version accepted for publicatio
Branching ratios for the beta decay of 21Na
We have measured the beta-decay branching ratio for the transition from 21Na
to the first excited state of 21Ne. A recently published test of the standard
model, which was based on a measurement of the beta-nu correlation in the decay
of 21Na, depended on this branching ratio. However, until now only relatively
imprecise (and, in some cases, contradictory) values existed for it. Our new
result, 4.74(4)%, reduces but does not remove the reported discrepancy with the
standard model.Comment: Revtex4, 2 fig
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