A numerical fit of analytical to simulated density profiles in dark matter haloes

Analytical and geometrical properties of generalized power-law (GPL) density profiles are investigated in detail. In particular, a one-to-one correspondence is found between mathematical parameters and geometrical parameters. Then GPL density profiles are compared with simulated dark haloes (SDH) density profiles, and nonlinear least-absolute values and least-squares fits involving the above mentioned five parameters (RFSM5 method) are prescribed. More specifically, the sum of absolute values or squares of absolute logarithmic residuals is evaluated on a large number of points making a 5-dimension hypergrid, through a few iterations. The size is progressively reduced around a fiducial minimum, and superpositions on nodes of earlier hypergrids are avoided. An application is made to a sample of 17 SDHs on the scale of cluster of galaxies, within a flat $\Lambda$CDM cosmological model (Rasia et al. 2004). In dealing with the mean SDH density profile, a virial radius, averaged over the whole sample, is assigned, which allows the calculation of the remaining parameters. Using a RFSM5 method provides a better fit with respect to other methods. No evident correlation is found between SDH dynamical state (relaxed or merging) and asymptotic inner slope of the logarithmic density profile or (for SDH comparable virial masses) scaled radius. Mean values and standard deviations of some parameters are calculated, and a comparison with previous results is made with regard to the scaled radius. A certain degree of degeneracy is found in fitting GPL to SDH density profiles. If it is intrinsic to the RFSM5 method or it could be reduced by the next generation of high-resolution simulations, still remains an open question.Comment: 44 pages, 6 figures, updated version with recent results from high-resolution simulations (Diemand et al. 2004; Reed et al. 2005) included in the discussion; accepted for publication on SAJ (Serbian Astronomical Journal

Relations Between Quantum Maps and Quantum States

The relation between completely positive maps and compound states is investigated in terms of the notion of quantum conditional probability

Unital Positive Maps and Quantum States

We analyze the structure of the subset of states generated by unital completely positive quantum maps, A witness that certifies that a state does not belong to the subset generated by a given map is constructed. We analyse the representations of positive maps and their relation to quantum Perron-Frobenius theory.Comment: 14 page

Wigner's Problem and Alternative Commutation Relations for Quantum Mechanics

It is shown, that for quantum systems the vectorfield associated with the equations of motion may admit alternative Hamiltonian descriptions, both in the Schr\"odinger and Heisenberg pictures. We illustrate these ambiguities in terms of simple examples.Comment: Latex,14 pages,accepted by Int. Jour.Mod.Phy

Dark matter haloes: an additional criterion for the choice of fitting density profiles

Simulated dark matter haloes are fitted by self-similar, universal density profiles, where the scaled parameters depend only on a scaled (truncation) radius which, in turn, is supposed to be independent on the mass and the formation redshift. A criterion for the choice of the best fitting density profile is proposed, with regard to a set of high-resolution simulations, where some averaging procedure on scaled density profiles has been performed, in connection with a number of fitting density profiles. An application is made to a pair of sets each made of a dozen of high-resolution simulations, which are available in literature, in connection with two currently used fitting density profiles, where the dependence of the scaled radius on the mass and the formation redshift, may be neglected to a first extent. Some features of the early evolution of dark matter haloes represented by fitting density profiles, are discussed in the limit of the spherical top-hat model.Comment: 62 pages, 9 figures, accepted for publication on SAJ (Serbian Astronomical Journal), paragraph and reference added for section

Classical and Quantum Systems: Alternative Hamiltonian Descriptions

In complete analogy with the classical situation (which is briefly reviewed) it is possible to define bi-Hamiltonian descriptions for Quantum systems. We also analyze compatible Hermitian structures in full analogy with compatible Poisson structures.Comment: To appear on Theor. Math. Phy

The low-mass population of the Rho Ophiuchi molecular cloud

Star formation theories are currently divergent regarding the fundamental physical processes that dominate the substellar regime. Observations of nearby young open clusters allow the brown dwarf (BD) population to be characterised down to the planetary mass regime, which ultimately must be accommodated by a successful theory. We hope to uncover the low-mass population of the Rho Ophiuchi molecular cloud and investigate the properties of the newly found brown dwarfs. We use near-IR deep images (reaching completeness limits of approximately 20.5 mag in J, and 18.9 mag in H and Ks) taken with the Wide Field IR Camera (WIRCam) at the Canada France Hawaii Telescope (CFHT) to identify candidate members of Rho Oph in the substellar regime. A spectroscopic follow-up of a small sample of the candidates allows us to assess their spectral type, and subsequently their temperature and membership. We select 110 candidate members of the Rho Ophiuchi molecular cloud, from which 80 have not previously been associated with the cloud. We observed a small sample of these and spectroscopically confirm six new brown dwarfs with spectral types ranging from M6.5 to M8.25