5,527 research outputs found
The -eigenvalue problem on some new fuzzy spheres
We study the eigenvalue equation for the 'Cartesian coordinates' observables
on the fully -covariant fuzzy circle
() and on the fully
-covariant fuzzy 2-sphere
() introduced in [G. Fiore, F. Pisacane, J. Geom. Phys. 132 (2018),
423-451]. We show that the spectrum and eigenvectors of fulfill a number
of properties which are expected for 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
of the noncommutative torus. We show that such -modules
have a natural interpretation as Moyal deformations of vector bundles over an
elliptic curve , under the condition that the deformation parameter
and the modular parameter satisfy a non-trivial relation.Comment: 16 pages, no figures; v2: minor correction
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
Collective Phenomena in and 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-
behavior of the DIS structure functions (SF) and possible slow-down of the
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
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
Energy cutoff, effective theories, noncommutativity, fuzzyness: the case of O(D)-covariant fuzzy spheres
Projecting a quantum theory onto the Hilbert subspace of states with energies
below a cutoff may lead to an effective theory with modified
observables, including a noncommutative space(time). Adding a confining
potential well with a very sharp minimum on a submanifold of the
original space(time) may induce a dimensional reduction to a noncommutative
quantum theory on . Here in particular we briefly report on our application
of this procedure to spheres of radius
(): making and the depth of the well depend on (and
diverge with) we obtain new fuzzy spheres
covariant under the {\it full} orthogonal groups ; the
commutators of the coordinates depend only on the angular momentum, as in
Snyder noncommutative spaces. Focusing on , we also discuss uncertainty
relations, localization of states, diagonalization of the space coordinates and
construction of coherent states. As the Hilbert space
dimension diverges, , and we recover ordinary quantum
mechanics on . These models might be suggestive for effective models in
quantum field theory, quantum gravity or condensed matter physics.Comment: Latex file, 21 pages. Proceedings of Science Volume 376 - Corfu
Summer Institute 2019 "School and Workshops on Elementary Particle Physics
and Gravity" (CORFU2019) - Workshop on Quantum Geometry, Field Theory and
Gravit
- …