Non-ergodic states induced by impurity levels in quantum spin chains

The semi-infinite XY spin chain with an impurity at the boundary has been chosen as a prototype of interacting many-body systems to test for non-ergodic behavior. The model is exactly solvable in analytic way in the thermodynamic limit, where energy eigenstates and the spectrum are obtained in closed form. In addition of a continuous band, localized states may split off from the continuum, for some values of the impurity parameters. In the next step, after the preparation of an arbitrary non-equilibrium state, we observe the time evolution of the site magnetization. Relaxation properties are described by the long-time behavior, which is estimated using the stationary phase method. Absence of localized states defines an ergodic region in parameter space, where the system relaxes to a homogeneous magnetization. Out of this region, impurity levels split from the band, and localization phenomena may lead to non-ergodicity.Comment: 10 pages, 5 figures. arXiv admin note: substantial text overlap with arXiv:1703.0344

Probing equilibrium glass flow up to exapoise viscosities

Glasses are out-of-equilibrium systems aging under the crystallization threat. During ordinary glass formation, the atomic diffusion slows down rendering its experimental investigation impractically long, to the extent that a timescale divergence is taken for granted by many. We circumvent here these limitations, taking advantage of a wide family of glasses rapidly obtained by physical vapor deposition directly into the solid state, endowed with different "ages" rivaling those reached by standard cooling and waiting for millennia. Isothermally probing the mechanical response of each of these glasses, we infer a correspondence with viscosity along the equilibrium line, up to exapoise values. We find a dependence of the elastic modulus on the glass age, which, traced back to temperature steepness index of the viscosity, tears down one of the cornerstones of several glass transition theories: the dynamical divergence. Critically, our results suggest that the conventional wisdom picture of a glass ceasing to flow at finite temperature could be wrong.Comment: 4 figures and 1 supplementary figur

A generalization of the cumulant expansion. Application to a scale-invariant probabilistic model

As well known, cumulant expansion is an alternative way to moment expansion to fully characterize probability distributions provided all the moments exist. If this is not the case, the so called escort mean values (or q-moments) have been proposed to characterize probability densities with divergent moments [C. Tsallis et al, J. Math. Phys 50, 043303 (2009)]. We introduce here a new mathematical object, namely the q-cumulants, which, in analogy to the cumulants, provide an alternative characterization to that of the q-moments for the probability densities. We illustrate this new scheme on a recently proposed family of scale-invariant discrete probabilistic models [A. Rodriguez et al, J. Stat. Mech. (2008) P09006; R. Hanel et al, Eur. Phys. J. B 72, 263268 (2009)] having q-Gaussians as limiting probability distributions

Inequality of opportunity and growth

Theoretical and empirical studies exploring the effects of income inequality upon growth reach a disappointing inconclusive result. This paper postulates that one reason for this ambiguity is that income inequality is actually a composite measure of at least two different sorts of inequality: inequality of opportunity and inequality of returns to effort. These two types of inequality affect growth through opposite channels, so the relationship between income inequality and growth is positive or negative depending on which component is larger. We test this proposal using inequality-of-opportunity measures computed from the PSID database for 23 states of the U.S. in 1980 and 1990. We find robust support for a negative relationship between inequality of opportunity and growth, and a positive relationship between inequality of returns to effort and growth.income inequality; inequality of opportunity; economic growth.

A deep and wide-field view at the IC 2944 / 2948 complex in Centaurus

We employed the ESO MPI wide-field camera and obtained deep images in the VIc pass-bands in the region of the IC 2944/2948 complex (l ~ 294; b ~ -1), and complemented them with literature and archival data. We used this material to derive the photometric, spectroscopic and kinematic properties of the brightest (V < 16) stars in the region. The VI deep photometry on the other end, helped us to unravel the lower main sequence of a few, possibly physical, star groups in the area. Our analysis confirmed previous suggestions that the extinction toward this line of sight follows the normal law (Rv = 3.1). We could recognize B-type stars spread in distance from a few hundred pc to at least 2 kpc. We found two young groups (age ~ 3 Myr) located respectively at about 2.3 and 3.2 kpc from the Sun. They are characterized by a significant variable extinction (E(B-V) ranging from 0.28 to 0.45 mag), and host a significant pre-main sequence population. We computed the initial mass functions for these groups and obtained slopes Gamma from -0.94 to -1.02 (e_Gamma = 0.3), in a scale where the classical Salpeter law is -1.35. We estimated the total mass of both main stellar groups in ~ 1100$and ~ 500$ Mo, respectively. Our kinematic analysis indicated that both groups of stars deviate from the standard rotation curve of the Milky Way, in line with literature results for this specific Galactic direction. Finally, along the same line of sight we identified a third group of early-type stars located at ~ 8 kpc from the Sun. This group might be located in the far side of the Sagittarius-Carina spiral arm.Comment: 13 pages, 11 figures, accepted for publication in MNRA