The xix_i-eigenvalue problem on some new fuzzy spheres

We study the eigenvalue equation for the 'Cartesian coordinates' observables $x_i$ on the fully $O(2)$-covariant fuzzy circle $\{S^1_\Lambda\}_{\Lambda\in\mathbb{N}}$ ($i=1,2$) and on the fully $O(3)$-covariant fuzzy 2-sphere $\{S^2_\Lambda\}_{\Lambda\in\mathbb{N}}$ ($i=1,2,3$) introduced in [G. Fiore, F. Pisacane, J. Geom. Phys. 132 (2018), 423-451]. We show that the spectrum and eigenvectors of $x_i$ fulfill a number of properties which are expected for $x_i$ to approximate well the corresponding coordinate operator of a quantum particle forced to stay on the unit sphere.Comment: 28 pages. Version 3: some misprints are correcte

New fuzzy spheres through confining potentials and energy cutoffs

We briefly report our recent construction of new fuzzy spheres of dimensions d=1,2 covariant under the full orthogonal group O(D), D=d+1. They are built by imposing a suitable energy cutoff on a quantum particle in D dimensions subject to a confining potential well V(r) with a very sharp minimum on the sphere of radius r=1; furthermore, the cutoff and the depth of the well depend on (and diverge with) a natural number L. The commutator of the coordinates depends only on the angular momentum, as in Snyder noncommutative spaces. When L diverges, the Hilbert space dimension diverges, too; S^d_L converges to S^d, and we recover ordinary quantum mechanics on S^d. These models might be useful in quantum field theory, quantum gravity or condensed matter physics.Comment: Latex file, 13 pages, 2 figures. Contribution to the proceedings of the Corfu Summer Institute "School and Workshops on Elementary Particle Physics and Gravity", 2-28 September 2017, Corfu, Greece. Version 3: some misprints in the published version are correcte

Fuzzy circle and new fuzzy sphere through confining potentials and energy cutoffs

Guided by ordinary quantum mechanics we introduce new fuzzy spheres of dimensions d=1,2: we consider an ordinary quantum particle in D=d+1 dimensions subject to a rotation invariant potential well V(r) with a very sharp minimum on a sphere of unit radius. Imposing a sufficiently low energy cutoff to `freeze' the radial excitations makes only a finite-dimensional Hilbert subspace accessible and on it the coordinates noncommutative \`a la Snyder; in fact, on it they generate the whole algebra of observables. The construction is equivariant not only under rotations - as Madore's fuzzy sphere -, but under the full orthogonal group O(D). Making the cutoff and the depth of the well dependent on (and diverging with) a natural number L, and keeping the leading terms in 1/L, we obtain a sequence S^d_L of fuzzy spheres converging (in a suitable sense) to the sphere S^d as L diverges (whereby we recover ordinary quantum mechanics on S^d). These models may be useful in condensed matter problems where particles are confined on a sphere by an (at least approximately) rotation-invariant potential, beside being suggestive of analogous mechanisms in quantum field theory or quantum gravity.Comment: Latex file, 43 pages, 2 figures. We have added references and made other minor improvements. To appear in J. Geom. Phy

Modules over the Noncommutative Torus and Elliptic Curves

Using the Weil-Brezin-Zak transform of solid state physics, we describe line bundles over elliptic curves in terms of Weyl operators. We then discuss the connection with finitely-generated projective modules over the algebra $A_\theta$ of the noncommutative torus. We show that such $A_\theta$-modules have a natural interpretation as Moyal deformations of vector bundles over an elliptic curve $E_\tau$, under the condition that the deformation parameter $\theta$ and the modular parameter $\tau$ satisfy a non-trivial relation.Comment: 16 pages, no figures; v2: minor correction

Collective Phenomena in pppp and epep Scattering

Bjorken scaling violation in deep inelastic electron-proton scattering (DIS) is related to the rise of hadronic cross sections by using the additive quark model. Of special interest is the connection between saturation in the low-$x$ behavior of the DIS structure functions (SF) and possible slow-down of the $pp$ cross section rise due to saturation effects. We also identify saturation effects in the DIS SF with phase transition that can be described by the Van der Waals equation of state.Comment: 4 pages, 1 figure; presented by L. Jenkovszky at "Diffraction 2016", International Workshop on Diffraction in High-Energy Physics, Acireale (Catania, Sicily), Sept. 2-8, 2016; to be published in the conference proceedings by AI

Reconstructing directed and weighted topologies of phase-locked oscillator networks

The formalism of complex networks is extensively employed to describe the dynamics of interacting agents in several applications. The features of the connections among the nodes in a network are not always provided beforehand, hence the problem of appropriately inferring them often arises. Here, we present a method to reconstruct directed and weighted topologies (REDRAW) of networks of heterogeneous phase-locked nonlinear oscillators. We ultimately plan on using REDRAW to infer the interaction structure in human ensembles engaged in coordination tasks, and give insights into the overall behavior

On complex power nonnegative matrices

Power nonnegative matrices are defined as complex matrices having at least one nonnegative integer power. We exploit the possibility of deriving a Perron Frobenius-like theory for these matrices, obtaining three main results and drawing several consequences. We study, in particular, the relationships with the set of matrices having eventually nonnegative powers, the inverse of M-type matrices and the set of matrices whose columns (rows) sum up to one

Do we really need regional innovation agencies? Some insights from the experience of an Italian region

Increasing globalization, if properly exploited, can provide interesting opportunities for regional economies. Nevertheless, when they are not managed with a far-sighted approach, regions, and particularly those at an intermediate level of development, can lose their comparative advantages compared to regions of developing countries. Innovation is the main instrument for improving and ensuring competitiveness to enterprises and growth opportunities to local economies. The aim of this paper is to discuss the importance of public policies in reinforcing regional innovation systems, and the role of regional innovation agencies. With this in mind, we describe the policies implemented by the Regional Agency for Technology and Innovation (ARTI) of Apulia, a region in Southern Italy. We also provide the first assessment of ARTI’s activities and provide some suggestions on how to improve regional R&D policies.public policy; innovation; regional innovation system; regional competitiveness

Optimal Content Downloading in Vehicular Networks

We consider a system where users aboard communication-enabled vehicles are interested in downloading different contents from Internet-based servers. This scenario captures many of the infotainment services that vehicular communication is envisioned to enable, including news reporting, navigation maps and software updating, or multimedia file downloading. In this paper, we outline the performance limits of such a vehicular content downloading system by modelling the downloading process as an optimization problem, and maximizing the overall system throughput. Our approach allows us to investigate the impact of different factors, such as the roadside infrastructure deployment, the vehicle-to-vehicle relaying, and the penetration rate of the communication technology, even in presence of large instances of the problem. Results highlight the existence of two operational regimes at different penetration rates and the importance of an efficient, yet 2-hop constrained, vehicle-to-vehicle relaying