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

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

A statistical test on the reliability of the non-coevality of stars in binary systems

We develop a statistical test on the expected difference in age estimates of two coeval stars in detached double-lined eclipsing binary systems that are only caused by observational uncertainties. We focus on stars in the mass range [0.8; 1.6] Msun, and on stars in the main-sequence phase. The ages were obtained by means of the maximum-likelihood SCEPtER technique. The observational constraints used in the recovery procedure are stellar mass, radius, effective temperature, and metallicity [Fe/H]. We defined the statistic W computed as the ratio of the absolute difference of estimated ages for the two stars over the age of the older one. We determined the critical values of this statistics above which coevality can be rejected. The median expected difference in the reconstructed age between the coeval stars of a binary system -- caused alone by the observational uncertainties -- shows a strong dependence on the evolutionary stage. This ranges from about 20% for an evolved primary star to about 75% for a near ZAMS primary. The median difference also shows an increase with the mass of the primary star from 20% for 0.8 Msun stars to about 50% for 1.6 Msun stars. The reliability of these results was checked by repeating the process with a grid of stellar models computed by a different evolutionary code. We show that the W test is much more sensible to age differences in the binary system components than the alternative approach of comparing the confidence interval of the age of the two stars. We also found that the distribution of W is, for almost all the examined cases, well approximated by beta distributions. The proposed method improves upon the techniques that are commonly adopted for judging the coevality of an observed system. It also provides a result founded on reliable statistics that simultaneously accounts for all the observational uncertainties.Comment: Abstract shortened. Accepted for publication in A&A. One reference fixe

The Pisa Stellar Evolution Data Base for low-mass stars

The last decade showed an impressive observational effort from the photometric and spectroscopic point of view for ancient stellar clusters in our Galaxy and beyond. The theoretical interpretation of these new observational results requires updated evolutionary models and isochrones spanning a wide range of chemical composition. With this aim we built the new "Pisa Stellar Evolution Database" of stellar models and isochrones by adopting a well-tested evolutionary code (FRANEC) implemented with updated physical and chemical inputs. In particular, our code adopts realistic atmosphere models and an updated equation of state, nuclear reaction rates and opacities calculated with recent solar elements mixture. A total of 32646 models have been computed in the range of initial masses 0.30 - 1.10 Msun for a grid of 216 chemical compositions with the fractional metal abundance in mass, Z, ranging from 0.0001 to 0.01, and the original helium content, Y, from 0.25 to 0.42. Models were computed for both solar-scaled and alpha-enhanced abundances with different external convection efficiencies. Correspondingly, 9720 isochrones were computed in the age range 8 - 15 Gyr, in time steps of 0.5 Gyr. The whole database is available to the scientific community on the web. Models and isochrones were compared with recent calculations available in the literature and with the color-magnitude diagram of selected Galactic globular clusters. The dependence of relevant evolutionary quantities on the chemical composition and convection efficiency were analyzed in a quantitative statistical way and analytical formulations were made available for reader's convenience.Comment: Accepted for publication in A&

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

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&

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

Calibrating convective-core overshooting with eclipsing binary systems. The case of low-mass main-sequence stars

In a robust statistical way, we quantify the uncertainty that affects the calibration of the overshooting efficiency parameter $\beta$ that is owing to the uncertainty on the observational data in double-lined eclipsing binary systems. We also quantify the bias that is caused by the lack of constraints on the initial helium content and on the efficiencies of the superadiabatic convection and microscopic diffusion. We adopted a modified grid-based SCEPtER pipeline using as observational constraints the effective temperatures, [Fe/H], masses, and radii of the two stars. In a reference scenario of mild overshooting $\beta = 0.2$ for the synthetic data, we found both large statistical uncertainties and biases on the estimated $\beta$. For the first 80% of the MS evolution, $\beta$ is biased and practically unconstrained in the whole explored range [0.0; 0.4]. In the last 5% of the MS the bias vanishes and the $1 \sigma$ error is about 0.05. For synthetic data computed with $\beta = 0.0$, the estimated $\beta$ is biased by about 0.12 in the first 80% of the MS evolution, and by 0.05 afterwards. Assuming an uncertainty of $\pm 1$ in the helium-to-metal enrichment ratio $\Delta Y/\Delta Z$, we found that in the terminal part of the MS evolution the error on the estimated $\beta$ values ranges from -0.05 to +0.10, while $\beta$ is basically unconstrained throughout the explored range at earlier evolutionary stages. A uniform variation of $\pm 0.24$ in the mixing-length parameter around the solar-calibrated value causes in last 5% of the MS an uncertainty from -0.09 to +0.15. A complete neglect of diffusion in the stellar evolution computations produces a $1 \sigma$ uncertainty of $\pm 0.08$ in the last 5% of the MS, while $\beta$ is practically unconstrained in the first 80% of the MS. Overall, the calibration appears poorly reliable.Comment: Abstract abridged; accepted for publication in A&