A general correlation inequality and the Almost Sure Local Limit Theorem for random sequences in the domain of attraction of a stable law

In the present paper we obtain a new correlation inequality and use it for the purpose of extending the theory of the Almost Sure Local Limit Theorem to the case of lattice random sequences in the domain of attraction of a stable law. In particular, we prove ASLLT in the case of the normal domain of attraction of $\alpha$--stable law, $\alpha\in(1,2)$

Edge insulating topological phases in a two-dimensional long-range superconductor

We study the zero-temperature phase diagram of a two dimensional square lattice loaded by spinless fermions, with nearest neighbor hopping and algebraically decaying pairing. We find that for sufficiently long-range pairing, new phases, not continuously connected with any short-range phase, occur, signaled by the violation of the area law for the Von Neumann entropy, by semi-integer Chern numbers, and by edge modes with nonzero mass. The latter feature results in the absence of single-fermion edge conductivity, present instead in the short- range limit. The definition of a topology in the bulk and the presence of a bulk-boundary correspondence is still suggested for the long-range phases. Recent experimental proposals and advances open the stimulating possibility to probe the described long-range effects in next-future realistic set-ups

Anderson localization of pairs in bichromatic optical lattices

We investigate the formation of bound states made of two interacting atoms moving in a one dimensional (1D) quasi-periodic optical lattice. We derive the quantum phase diagram for Anderson localization of both attractively and repulsively bound pairs. We calculate the pair binding energy and show analytically that its behavior as a function of the interaction strength depends crucially on the nature -extended, multi-fractal, localized- of the single-particle atomic states. Experimental implications of our results are discussed.Comment: final revised version with more explanations, 4 pages, 3 figure

Food waste materials appear efficient and low-cost adsorbents for the removal of organic and inorganic pollutants from wastewater

In recent studies, the adsorption capacity of several food waste materials has been assessed by performing adsorption experiments in heterogeneous operating conditions. In a latest study, the efficiency of such food waste materials for the removal of metals and metalloids from complex multi-element solutions was evaluated in homogeneous experimental conditions, which allowed comparing the adsorption capacities of the individual adsorbents. Considering the high efficiency of the examined low-cost adsorbents for the removal of inorganic pollutants, preliminary studies were conducted in our lab for assessing the potential of the investigated food waste materials to adsorb volatile organic compounds from a real polluted matrix of leachate. Some recent studies have shown the efficiency of low cost materials for the removal of industrial organic dyes, polycyclic aromatic hydrocarbons and phenolic compounds. However, the food waste adsorbents’ efficiency for the removal of volatile organic compounds was not investigated. Our preliminary studies showed good adsorption capacities of the examined food waste materials for aliphatic and aromatic hydrocarbons. Therefore, it is worth to carry out further studies about volatile organic compounds’ removal by food waste adsorbents

The observed chemical structure of L1544

Prior to star formation, pre-stellar cores accumulate matter towards the centre. As a consequence, their central density increases while the temperature decreases. Understanding the evolution of the chemistry and physics in this early phase is crucial to study the processes governing the formation of a star. We aim at studying the chemical differentiation of a prototypical pre-stellar core, L1544, by detailed molecular maps. In contrast with single pointing observations, we performed a deep study on the dependencies of chemistry on physical and external conditions. We present the emission maps of 39 different molecular transitions belonging to 22 different molecules in the central 6.25 arcmin$^2$ of L1544. We classified our sample in five families, depending on the location of their emission peaks within the core. Furthermore, to systematically study the correlations among different molecules, we have performed the principal component analysis (PCA) on the integrated emission maps. The PCA allows us to reduce the amount of variables in our dataset. Finally, we compare the maps of the first three principal components with the H$_2$ column density map, and the T$_{dust}$ map of the core. The results of our qualitative analysis is the classification of the molecules in our dataset in the following groups: (i) the $c$-C$_3$H$_2$ family (carbon chain molecules), (ii) the dust peak family (nitrogen-bearing species), (iii) the methanol peak family (oxygen-bearing molecules), (iv) the HNCO peak family (HNCO, propyne and its deuterated isotopologues). Only HC$^{18}$O$^+$ and $^{13}$CS do not belong to any of the above mentioned groups. The principal component maps allow us to confirm the (anti-)correlations among different families that were described in a first qualitative analysis, but also points out the correlation that could not be inferred before.Comment: 29 pages, 19 figures, 2 appendices, accepted for publication in A&A, arXiv abstract has been slightly modifie

Thermodynamic Bounds on Efficiency for Systems with Broken Time-reversal Symmetry

We show that for systems with broken time-reversal symmetry the maximum efficiency and the efficiency at maximum power are both determined by two parameters: a "figure of merit" and an asymmetry parameter. In contrast to the time-symmetric case, the figure of merit is bounded from above; nevertheless the Carnot efficiency can be reached at lower and lower values of the figure of merit and far from the so-called strong coupling condition as the asymmetry parameter increases. Moreover, the Curzon-Ahlborn limit for efficiency at maximum power can be overcome within linear response. Finally, always within linear response, it is allowed to have simultaneously Carnot efficiency and non-zero power.Comment: Final version, 4 pages, 3 figure

A study of the cc-C3HD\mathrm{C_{3}HD}/cc-C3H2\mathrm{C_{3}H_{2}} ratio in low-mass star forming regions

We use the deuteration of $c$-$\mathrm{C_{3}H_{2}}$ to probe the physical parameters of starless and protostellar cores, related to their evolutionary states, and compare it to the $\mathrm{N_{2}H^{+}}$-deuteration in order to study possible differences between the deuteration of C- and N-bearing species. We observed the main species $c$-$\mathrm{C_{3}H_{2}}$, the singly and doubly deuterated species $c$-$\mathrm{C_{3}HD}$ and $c$-$\mathrm{C_{3}D_{2}}$, as well as the isotopologue $c$-$\mathrm{{H^{13}CC_{2}H}}$ toward 10 starless cores and 5 protostars in the Taurus and Perseus Complexes. We examined the correlation between the $N$($c$-$\mathrm{C_{3}HD}$)/$N$($c$-$\mathrm{C_{3}H_{2}}$) ratio and the dust temperature along with the $\mathrm{H_2}$ column density and the CO depletion factor. The resulting $N$($c$-$\mathrm{C_{3}HD}$)/$N$($c$-$\mathrm{C_{3}H_{2}}$) ratio is within the error bars consistent with $10\%$ in all starless cores with detected $c$-$\mathrm{C_{3}HD}$. This also accounts for the protostars except for the source HH211, where we measure a high deuteration level of $23\%$. The deuteration of $\mathrm{N_{2}H^{+}}$ follows the same trend but is considerably higher in the dynamically evolved core L1544. Toward the protostellar cores the coolest objects show the largest deuterium fraction in $c$-$\mathrm{C_{3}H_{2}}$. We show that the deuteration of $c$-$\mathrm{C_{3}H_{2}}$ can trace the early phases of star formation and is comparable to that of $\mathrm{N_{2}H^{+}}$. However, the largest $c$-$\mathrm{C_{3}H_{2}}$ deuteration level is found toward protostellar cores, suggesting that while $c$-$\mathrm{C_{3}H_{2}}$ is mainly frozen onto dust grains in the central regions of starless cores, active deuteration is taking place on ice