The genus of the configuration spaces for Artin groups of affine type

Let $(W,S)$ be a Coxeter system, $S$ finite, and let $G_{W}$ be the associated Artin group. One has configuration spaces $Y,\ Y_{W},$ where $G_{W}=\pi_1(Y_{W}),$ and a natural $W$-covering $f_{W}:\ Y\to Y_{W}.$ The Schwarz genus $g(f_{W})$ is a natural topological invariant to consider. In this paper we generalize this result by computing the Schwarz genus for a class of Artin groups, which includes the affine-type Artin groups. Let $K=K(W,S)$ be the simplicial scheme of all subsets $J\subset S$ such that the parabolic group $W_J$ is finite. We introduce the class of groups for which $dim(K)$ equals the homological dimension of $K,$ and we show that $g(f_{W})$ is always the maximum possible for such class of groups. For affine Artin groups, such maximum reduces to the rank of the group. In general, it is given by $dim(X_{W})+1,$ where $X_{ W}\subset Y_{ W}$ is a well-known $CW$-complex which has the same homotopy type as $Y_{ W}.$Comment: To appear in Atti Accad. Naz. Lincei Rend. Lincei Mat. App

Superconductivity emerging from an electronic phase separation in the charge ordered phase of RbFe2_2As2_2

$^{75}$As, $^{87}$Rb and $^{85}$Rb nuclear quadrupole resonance (NQR) and $^{87}$Rb nuclear magnetic resonance (NMR) measurements in RbFe$_2$As$_2$ iron-based superconductor are presented. We observe a marked broadening of $^{75}$As NQR spectrum below $T_0\simeq 140$ K which is associated with the onset of a charge order in the FeAs planes. Below $T_0$ we observe a power-law decrease in $^{75}$As nuclear spin-lattice relaxation rate down to $T^*\simeq 20$ K. Below that temperature the nuclei start to probe different dynamics owing to the different local electronic configurations induced by the charge order. A fraction of the nuclei probes spin dynamics associated with electrons approaching a localization while another fraction probes activated dynamics possibly associated with a pseudogap. These different trends are discussed in the light of an orbital selective behaviour expected for the electronic correlations.Comment: 5 pages, 3 figures and 4 pages of supplemental materia

Phase diagram of soft-core bosons in two dimensions

The low temperature phase diagram of Bose soft disks in two dimensions is studied by numerical simulations. It is shown that a supersolid cluster phase exists, within a range of the model parameters, analogous to that recently observed for a system of aligned dipoles interacting via a softened potential at short distance. These findings indicate that a long-range tail of the interaction is unneeded to obtain such a phase, and that the soft-core repulsive interaction is the minimal model for supersolidity

Imaginary Time Correlations and the phaseless Auxiliary Field Quantum Monte Carlo

The phaseless Auxiliary Field Quantum Monte Carlo method provides a well established approximation scheme for accurate calculations of ground state energies of many-fermions systems. Here we apply the method to the calculation of imaginary time correlation functions. We give a detailed description of the technique and we test the quality of the results for static and dynamic properties against exact values for small systems.Comment: 13 pages, 6 figures; submitted to J. Chem. Phy

Dynamic structure factor for 3He in two-dimensions

Recent neutron scattering experiments on 3He films have observed a zero-sound mode, its dispersion relation and its merging with -and possibly emerging from- the particle-hole continuum. Here we address the study of the excitations in the system via quantum Monte Carlo methods: we suggest a practical scheme to calculate imaginary time correlation functions for moderate-size fermionic systems. Combined with an efficient method for analytic continuation, this scheme affords an extremely convincing description of the experimental findings.Comment: 5 pages, 5 figure

On the age of Galactic bulge microlensed dwarf and subgiant stars

Recent results by Bensby and collaborators on the ages of microlensed stars in the Galactic bulge have challenged the picture of an exclusively old stellar population. However, these age estimates have not been independently confirmed. In this paper we verify these results by means of a grid-based method and quantify the systematic biases that might be induced by some assumptions adopted to compute stellar models. We explore the impact of increasing the initial helium abundance, neglecting the element microscopic diffusion, and changing the mixing-length calibration in theoretical stellar track computations. We adopt the SCEPtER pipeline with a novel stellar model grid for metallicities [Fe/H] from -2.00 to 0.55 dex, and masses in the range [0.60; 1.60] Msun from the ZAMS to the helium flash at the red giant branch tip. We show for the considered evolutionary phases that our technique provides unbiased age estimates. Our age results are in good agreement with Bensby and collaborators findings and show 16 stars younger than 5 Gyr and 28 younger than 9 Gyr over a sample of 58. The effect of a helium enhancement as large as Delta Y/Delta Z = 5 is quite modest, resulting in a mean age increase of metal rich stars of 0.6 Gyr. Even simultaneously adopting a high helium content and the upper values of age estimates, there is evidence of 4 stars younger than 5 Gyr and 15 younger than 9 Gyr. For stars younger than 5 Gyr, the use of stellar models computed by neglecting microscopic diffusion or by assuming a super-solar mixing-length value leads to a mean increase in the age estimates of about 0.4 Gyr and 0.5 Gyr respectively. Even considering the upper values for the age estimates, there are four stars estimated younger than 5 Gyr is in both cases. Thus, the assessment of a sizeable fraction of young stars among the microlensed sample in the Galactic bulge appears robust.Comment: Accepted for publication in A&A. Abstract shortene

Cumulative physical uncertainty in modern stellar models. II. The dependence on the chemical composition

We extend our work on the effects of the uncertainties on the main input physics for the evolution of low-mass stars. We analyse the dependence of the cumulative physical uncertainty affecting stellar tracks on the chemical composition. We calculated more than 6000 stellar tracks and isochrones, with metallicity ranging from Z = 0.0001 to 0.02, by changing the following physical inputs within their current range of uncertainty: 1H(p,nu e+)2H, 14N(p,gamma)15O and triple-alpha reaction rates, radiative and conductive opacities, neutrino energy losses, and microscopic diffusion velocities. The analysis was performed using a latin hypercube sampling design. We examine in a statistical way the dependence on the variation of the physical inputs of the turn-off (TO) luminosity, the central hydrogen exhaustion time (t_H), the luminosity and the helium core mass at the red-giant branch (RGB) tip, and the zero age horizontal branch (ZAHB) luminosity in the RR Lyrae region. For the stellar tracks, an increase from Z = 0.0001 to Z = 0.02 produces a cumulative physical uncertainty in TO luminosity from 0.028 dex to 0.017 dex, while the global uncertainty on t_H increases from 0.42 Gyr to 1.08 Gyr. For the RGB tip, the cumulative uncertainty on the luminosity is almost constant at 0.03 dex, whereas the one the helium core mass decreases from 0.0055 M_sun to 0.0035 M_sun. The dependence of the ZAHB luminosity error is not monotonic with Z, and it varies from a minimum of 0.036 dex at Z = 0.0005 to a maximum of 0.047 dex at Z = 0.0001. Regarding stellar isochrones of 12 Gyr, the cumulative physical uncertainty on the predicted TO luminosity and mass increases respectively from 0.012 dex to 0.014 dex and from 0.0136 M_sun to 0.0186 M_sun. Consequently, for ages typical of galactic globular clusters, the uncertainty on the age inferred from the TO luminosity increases from 325 Myr to 415 Myr.Comment: Accepted for publication in A&