Extremal covariant quantum operations and POVM's

We consider the convex sets of QO's (quantum operations) and POVM's (positive operator valued measures) which are covariant under a general finite-dimensional unitary representation of a group. We derive necessary and sufficient conditions for extremality, and give general bounds for ranks of the extremal POVM's and QO's. Results are illustrated on the basis of simple examples.Comment: 18 pages, to appear on J. Math. Phy

Hubble constant and dark energy inferred from free-form determined time delay distances

Time delays between multiple images of lensed sources can probe the geometry of the universe. We propose a novel method based on free-form modelling of gravitational lenses to estimate time-delay distances and, in turn, cosmological parameters. This approach does not suffer from the degeneracy between the steepness of the profile and the cosmological parameters. We apply the method to 18 systems having time delay measurements and find H_0=69+-6(stat.)+-4(syst.) km s^{-1}Mpc^{-1}. In combination with WMAP9, the constraints on dark energy are Omega_w=0.68+-0.05 and w=-0.86+-0.17 in a flat model with constant equation-of-state.Comment: 6 pages; accepted for publication on MNRA

SIDIS in the target fragmentation region: polarized and transverse momentum dependent fracture functions

The target fragmentation region of semi-inclusive deep inelastic scattering is described at leading twist, taking beam and target polarizations into account. The formalism of polarized and transverse-momentum dependent fracture functions is developed and the observables for some specific processes are presented.Comment: 18 pages, 2 figures. Some equations modified and text shortened; main conclusions unchange

Chebyshev, Legendre, Hermite and other orthonormal polynomials in D-dimensions

We propose a general method to construct symmetric tensor polynomials in the D-dimensional Euclidean space which are orthonormal under a general weight. The D-dimensional Hermite polynomials are a particular case of the present ones for the case of a gaussian weight. Hence we obtain generalizations of the Legendre and of the Chebyshev polynomials in D dimensions that reduce to the respective well-known orthonormal polynomials in D=1 dimensions. We also obtain new D-dimensional polynomials orthonormal under other weights, such as the Fermi-Dirac, Bose-Einstein, Graphene equilibrium distribution functions and the Yukawa potential. We calculate the series expansion of an arbitrary function in terms of the new polynomials up to the fourth order and define orthonormal multipoles. The explicit orthonormalization of the polynomials up to the fifth order (N from 0 to 4) reveals an increasing number of orthonormalization equations that matches exactly the number of polynomial coefficients indication the correctness of the present procedure.Comment: 20 page

Abelian versus non-Abelian Baecklund Charts: some remarks

Connections via Baecklund transformations among different non-linear evolution equations are investigated aiming to compare corresponding Abelian and non Abelian results. Specifically, links, via Baecklund transformations, connecting Burgers and KdV-type hierarchies of nonlinear evolution equations are studied. Crucial differences as well as notable similarities between Baecklund charts in the case of the Burgers - heat equation, on one side and KdV -type equations are considered. The Baecklund charts constructed in [16] and [17], respectively, to connect Burgers and KdV-type hierarchies of operator nonlinear evolution equations show that the structures, in the non-commutative cases, are richer than the corresponding commutative ones.Comment: 18 page