Propositional computability logic I

In the same sense as classical logic is a formal theory of truth, the recently initiated approach called computability logic is a formal theory of computability. It understands (interactive) computational problems as games played by a machine against the environment, their computability as existence of a machine that always wins the game, logical operators as operations on computational problems, and validity of a logical formula as being a scheme of "always computable" problems. The present contribution gives a detailed exposition of a soundness and completeness proof for an axiomatization of one of the most basic fragments of computability logic. The logical vocabulary of this fragment contains operators for the so called parallel and choice operations, and its atoms represent elementary problems, i.e. predicates in the standard sense. This article is self-contained as it explains all relevant concepts. While not technically necessary, however, familiarity with the foundational paper "Introduction to computability logic" [Annals of Pure and Applied Logic 123 (2003), pp.1-99] would greatly help the reader in understanding the philosophy, underlying motivations, potential and utility of computability logic, -- the context that determines the value of the present results. Online introduction to the subject is available at http://www.cis.upenn.edu/~giorgi/cl.html and http://www.csc.villanova.edu/~japaridz/CL/gsoll.html .Comment: To appear in ACM Transactions on Computational Logi

Kohn-Sham calculations combined with an average pair-density functional theory

A recently developed formalism in which Kohn-Sham calculations are combined with an ``average pair density functional theory'' is reviewed, and some new properties of the effective electron-electron interaction entering in this formalism are derived. A preliminary construction of a fully self-consitent scheme is also presented in this framework.Comment: submitted to Int. J. Mod. Phys. B (proceedings of the 30th International Workshop on Condensed Matter Theories

NGC 4337: an over-looked old cluster in the inner disc of the Milky Way

Galactic open clusters do not survive long in the high density regions of the inner Galactic disc. Inside the solar ring only 11 open clusters are known with ages older than one Gyr. We show here, basing on deep, high-quality photometry, that NGC 4337, contrary to earlier findings, is indeed an old open cluster. The cluster is located very close to the conspicuous star cluster Trumpler 20, as well mis-classified in the past, and that has received so much attention in recent years. NGC 4337 shows a significant clump of He-burning stars which was not detected previously. Its beautiful color-magnitude diagram is strikingly similar to the one of the classical old open clusters IC 4651, NGC 752, and NGC 3680, and this suggests similar age and composition. A spectroscopic study is much needed to confirm our findings. This, in turn, would also allow us to better define the inner disc radial abundance gradient and its temporal evolution.To this aim, a list of clump star candidates is provided.Comment: 5 pages, 4 eps figures, in press as MNRAS Lette

Quantum correlation dynamics in photosynthetic processes assisted by molecular vibrations

During the long course of evolution, nature has learnt how to exploit quantum effects. In fact, recent experiments reveal the existence of quantum processes whose coherence extends over unexpectedly long time and space ranges. In particular, photosynthetic processes in light-harvesting complexes display a typical oscillatory dynamics ascribed to quantum coherence. Here, we consider the simple model where a dimer made of two chromophores is strongly coupled with a quasi-resonant vibrational mode. We observe the occurrence of wide oscillations of genuine quantum correlations, between electronic excitations and the environment, represented by vibrational bosonic modes. Such a quantum dynamics has been unveiled through the calculation of the negativity of entanglement and the discord, indicators widely used in quantum information for quantifying the resources needed to realize quantum technologies. We also discuss the possibility of approximating additional weakly-coupled off-resonant vibrational modes, simulating the disturbances induced by the rest of the environment, by a single vibrational mode. Within this approximation, one can show that the off-resonant bath behaves like a classical source of noise

Maximally discordant mixed states of two qubits

We study the relative strength of classical and quantum correlations, as measured by discord, for two-qubit states. Quantum correlations appear only in the presence of classical correlations, while the reverse is not always true. We identify the family of states that maximize the discord for a given value of the classical correlations and show that the largest attainable discord for mixed states is greater than for pure states. The difference between discord and entanglement is emphasized by the remarkable fact that these states do not maximize entanglement and are, in some cases, even separable. Finally, by random generation of density matrices uniformly distributed over the whole Hilbert space, we quantify the frequency of the appearance of quantum and classical correlations for different ranks

The thickening of the thin disk in the third Galactic quadrant

In the third Galactic quadrant (180 < l < 270) of the Milky Way, the Galactic thin disk exhibits a significant warp ---shown both by gas and young stars--- bending down a few kpc below the formal Galactic plane (b=0). This warp shows its maximum at 240, in the direction of the Canis Major constellation. In a series of papers we have traced the detailed structure of this region using open star clusters, putting particular emphasis on the spiral structure of the outer disk. We noticed a conspicuous accumulation of young star clusters within 2-3 kpc from the Sun and close to b=0, that we interpreted as the continuation of the Local (Orion) arm towards the outer disk. While most clusters (and young stars in their background) follow closely the warp of the disk, our decade-old survey of the spiral structure of this region led us to identify three clusters, Haffner~18(1 and 2) and Haffner~19, which remain very close to b=0 and lie at distances (4.5, 8.0, and 6.4 kpc) where most of the material is already significantly warped. Here we report on a search for clusters that share the same properties as Haffner~18 and 19, and investigate the possible reasons for such an unexpected occurrence. We present UBVRI photometry of 5~young clusters, namely NGC~2345, NGC~2374, Trumpler~9, Haffner~20, and Haffner~21, which also lie close to the formal Galactic plane. With the exception of Haffner~20, in the background of these clusters we detected young stars that appear close to b=0, and are located at distances up to 8 kpc from the Sun, thus deviating significantly from the warp. These populations define a structure that distributes over almost the entire third Galactic quadrant. We discuss this structure in the context of a possible thin disk flaring, in full similarity with the Galactic thick disk.Comment: 53 pages, 12 eps figures, in press in the Astronomical Journa

CO2 lidar system for atmospheric studies

A lidar facility using a TEA CO2 laser source is being developed at the ENEA Laboratories for Atmospheric Studies. The different subsystems and the proposed experimental activities are described

Spiral structure of the Third Galactic Quadrant and the solution to the Canis Major debate

With the discovery of the Sagittarius dwarf spheroidal (Ibata et al. 1994), a galaxy caught in the process of merging with the Milky Way, the hunt for other such accretion events has become a very active field of astrophysical research. The identification of a stellar ring-like structure in Monoceros, spanning more than 100 degrees (Newberg et al. 2002), and the detection of an overdensity of stars in the direction of the constellation of Canis Major (CMa, Martin et al. 2004), apparently associated to the ring, has led to the widespread belief that a second galaxy being cannibalised by the Milky Way had been found. In this scenario, the overdensity would be the remaining core of the disrupted galaxy and the ring would be the tidal debris left behind. However, unlike the Sagittarius dwarf, which is well below the Galactic plane and whose orbit, and thus tidal tail, is nearly perpendicular to the plane of the Milky Way, the putative CMa galaxy and ring are nearly co-planar with the Galactic disk. This severely complicates the interpretation of observations. In this letter, we show that our new description of the Milky Way leads to a completely different picture. We argue that the Norma-Cygnus spiral arm defines a distant stellar ring crossing Monoceros and the overdensity is simply a projection effect of looking along the nearby local arm. Our perspective sheds new light on a very poorly known region, the third Galactic quadrant (3GQ), where CMa is located.Comment: 5 pages, 2 figures. Quality of Fig 1 has been degraded to make it smaller. Original fig. available on request. accepted for publication in MNRAS letter