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