Albanese and Picard 1-motives

We define, in a purely algebraic way, 1-motives $Alb^{+}(X)$, $Alb^{-}(X)$, $Pic^{+}(X)$ and $Pic^{-}(X)$ associated with any algebraic scheme $X$ over an algebraically closed field of characteristic zero. For $X$ over \C of dimension $n$ the Hodge realizations are, respectively, $H^{2n-1}(X)(n)$, $H_{1}(X)$, $H^{1}(X)(1)$ and $H_{2n-1}(X)(1-n)$.Comment: 5 pages, LaTeX, submitted as CR Not

Ab-initio Gorkov-Green's function calculations of open-shell nuclei

We present results from a new ab-initio method that uses the self-consistent Gorkov Green's function theory to address truly open-shell systems. The formalism has been recently worked out up to second order and is implemented here in nuclei for the first time on the basis of realistic nuclear forces. We find good convergence of the results with respect to the basis size in Ca44 and Ni74 and discuss quantities of experimental interest including ground-state energies, pairing gaps and particle addition/removal spectroscopy. These results demonstrate that the Gorkov method is a valid alternative to multireference approaches for tackling degenerate or near degenerate quantum systems. In particular, it increases the number of mid-mass nuclei accessible in an ab-initio fashion from a few tens to a few hundreds.Comment: 5 pages, 3 figure

Ab-initio self-consistent Gorkov-Green's function calculations of semi-magic nuclei - II. Numerical implementation at second order with a two-nucleon interaction

The newly developed Gorkov-Green's function approach represents a promising path to the ab initio description of medium-mass open-shell nuclei. We discuss the implementation of the method at second order with a two-body interaction, with particular attention to the numerical solution of Gorkov's equation. Different sources of theoretical error and degrees of self-consistency are investigated. We show that Krylov projection techniques with a multi-pivot Lanczos algorithm efficiently handle the growth of poles in the one-body Green's function when Gorkov's equation is solved self-consistently. The end result is a tractable, accurate and gently scaling ab initio scheme applicable to full isotopic chains in the medium-mass region.Comment: 17 pages, 13 figure

Non-perturbative calculation of the two-loop Lamb shift in Li-like ions

A calculation valid to all orders in the nuclear-strength parameter is presented for the two-loop Lamb shift, notably for the two-loop self-energy correction, to the 2p-2s transition energies in heavy Li-like ions. The calculation removes the largest theoretical uncertainty for these transitions and yields the first experimental identification of two-loop QED effects in the region of the strong binding field

Toward the Ab-initio Description of Medium Mass Nuclei

As ab-initio calculations of atomic nuclei enter the A=40-100 mass range, a great challenge is how to approach the vast majority of open-shell (degenerate) isotopes. We add realistic three-nucleon interactions to the state of the art many-body Green's function theory of closed-shells, and find that physics of neutron driplines is reproduced with very good quality. Further, we introduce the Gorkov formalism to extend ab-initio theory to semi-magic, fully open-shell, isotopes. Proof-of-principle calculations for Ca-44 and Ni-74 confirm that this approach is indeed feasible. Combining these two advances (open-shells and three-nucleon interactions) requires longer, technical, work but it is otherwise within reach.Comment: Contribution to Summary Report of EURISOL Topical and Town Meetings, 15-19 October 2012; missing affiliations added and corrected errors in Tab

Sustaining and enabling territorial resilience through making actions. The Make in Progress case study.

The recent evolution of production models within urban context shows a possible scenario characterized by new interactions between design-driven innovation, making, creativity and social innovation. The paper analyses this scenario combined with the idea of Territorial Capital as a model to study a specific territory (EU Leader Project; 1999)1 by looking at a case study : Make in Progress, which explores new models of interaction between creative industries, makers, DIY people, artisan and SMEs within urban area and industrial district. The goal of this paper is to analyze how the phenomenon of Open Creative Lab (Ibert, 2015)2 can contribute to the resilience of the territories and how unexpected localized creative communities could emerge. To answer this question the paper focuses on the relationship and the potential of social innovation and service design (Meroni-Sangiorgi,20113; Stickdorn-Schneider,20124) in the territorial enhancement processes, through the making. In this case, the making gets the role of enabler in development of the territorial capital (Arquilla-Bianchini-Maffei-Carelli,20145), becoming from a purpose, as it often happens in most of the process of creation of making places such as fablab and makerspaces (Walter,20146; Gershenfeld,20077), to a real opportunity to be used to make the most interesting characteristics of a territory emerge: people and their capabilities. In detail, the case study of MakeinProgress (MiP) will be analyzed as an applied case of this theory. MIP is born from a real opportunity from the territory: the architectural recovery of the space of a former Filanda, totally funded by local and supralocal authorities by a process of public financing, in the beginning started as incubator and later converted by the intervention of design. We analyzed the territory, defined possible scenario, verified the applicability of this scenario by isolating potential of the area, modified and adapted scenario to the real potential of territory coming to set up an experimental model of action (MiP as demo service). Thanks to this activities was demonstrate how a laboratory in the suburbs, a suburb that did not imagine a possible development in creativity, acts as empowering latent elements showing unexpected capabilities and resilience

Radii and binding energies in oxygen isotopes: a puzzle for nuclear forces

We present a systematic study of both nuclear radii and binding energies in (even) oxygen isotopes from the valley of stability to the neutron drip line. Both charge and matter radii are compared to state-of-the-art {\it ab initio} calculations along with binding energy systematics. Experimental matter radii are obtained through a complete evaluation of the available elastic proton scattering data of oxygen isotopes. We show that, in spite of a good reproduction of binding energies, {\it ab initio} calculations with conventional nuclear interactions derived within chiral effective field theory fail to provide a realistic description of charge and matter radii. A novel version of two- and three-nucleon forces leads to considerable improvement of the simultaneous description of the three observables for stable isotopes, but shows deficiencies for the most neutron-rich systems. Thus, crucial challenges related to the development of nuclear interactions remain.Comment: 6 pages, 5 figures, Submitted to Nature Physics, April 12th 2016; first version (v1 Arxiv) Internal Report Preprint Irfu-18 December 2015. 6 p., 5 fig., Submitted to Physical Review Letters, April 29, May 3rd 2016; 2nd version. Int. Rep. Irfu-24 May 2016. Published in PRL, 27 July 2016 with the modified title (Radii and binding energies in oxygen isotopes: a challenge for nuclear forces

Nori 1-motives

Let EHM be Nori's category of effective homological mixed motives. In this paper, we consider the thick abelian subcategory EHM_1 generated by the i-th relative homology of pairs of varieties for i = 0,1. We show that EHM_1 is naturally equivalent to the abelian category M_1 of Deligne 1-motives with torsion; this is our main theorem. Along the way, we obtain several interesting results. Firstly, we realize M_1 as the universal abelian category obtained, using Nori's formalism, from the Betti representation of an explicit diagram of curves. Secondly, we obtain a conceptual proof of a theorem of Vologodsky on realizations of 1-motives. Thirdly, we verify a conjecture of Deligne on extensions of 1-motives in the category of mixed realizations for those extensions that are effective in Nori's sense

The Neron-Severi group of a proper seminormal complex variety

We prove a Lefschetz (1,1)-Theorem for proper seminormal varieties over the complex numbers. The proof is a non-trivial geometric argument applied to the isogeny class of the Lefschetz 1-motive associated to the mixed Hodge structure on H^2.Comment: 16 pages; Mathematische Zeitschrift (2008