On the canonical divisor of smooth toroidal compactifications

In this paper, we show that the canonical divisor of a smooth toroidal compactification of a complex hyperbolic manifold must be nef if the dimension is greater or equal to three. Moreover, if $n\geq 3$ we show that the numerical dimension of the canonical divisor of a smooth $n$-dimensional compactification is always bigger or equal to $n-1$. We also show that up to a finite \'etale cover all such compactifications have ample canonical class, therefore refining a classical theorem of Mumford and Tai. Finally, we improve in all dimensions $n\geq 3$ the cusp count for finite volume complex hyperbolic manifolds given in [DD15a].Comment: Title shortened to match published versio

Gamma-Ray Astronomy around 100 TeV with a large Muon Detector operated at Very High Altitude

Measurements at 100 TeV and above are an important goal for the next generation of high energy gamma-ray astronomy experiments to solve the still open problem of the origin of galactic cosmic rays. The most natural experimental solution to detect very low radiation fluxes is provided by the Extensive Air Shower (EAS) arrays. They benefit from a close to 90% duty cycle and a very large field of view (about 2 sr), but the sensitivity is limited by their angular resolution and their poor cosmic ray background discrimination. Above 10 TeV the standard technique for rejecting the hadronic background consists in looking for "muon-poor" showers. In this paper we discuss the capability of a large muon detector (A=2500 m2) operated with an EAS array at very high altitude (>4000 m a.s.l.) to detect gamma-ray fluxes around 100 TeV. Simulation-based estimates of energy ranges and sensitivities are presented.Comment: 4 pages, proceedings of the 30th ICRC, Merida, Mexico, 200

nZVI particles production for the remediation of soil and water polluted by inorganic Lead

The present study deals with experiments of Pb removal by nano-Zero Valent Iron (nZVI) in aqueous solution and in soil. Synthetic Pb aqueous solutions were treated by nZVI, at a fixed Pb concentration of 100 mg L-1 , varying nanoparticles initial concentration in the range between 27 and 270 mg nZVI L-1 . A kinetic study was carried out: Pb adsorption followed a first order kinetic, and half life times between 11 and 26.66 min were determined. Soil samples were first characterized, and Pb speciation and concentration by sequential extractions was determined. Adsorption tests were then carried out at three selected amounts of nZVI, to allow Pb stabilization in the soil matrix. To evaluate the treatment efficiency, sequential extractions were also performed on the treated samples

Characterizing topological order by studying the ground states of an infinite cylinder

Given a microscopic lattice Hamiltonian for a topologically ordered phase, we describe a tensor network approach to characterize its emergent anyon model and, in a chiral phase, also its gapless edge theory. First, a tensor network representation of a complete, orthonormal set of ground states on a cylinder of infinite length and finite width is obtained through numerical optimization. Each of these ground states is argued to have a different anyonic flux threading through the cylinder. In a chiral phase, the entanglement spectrum of each ground state is seen to reveal a different sector of the corresponding gapless edge theory. A quasi-orthogonal basis on the torus is then produced by chopping off and reconnecting the tensor network representation on the cylinder. Elaborating on the recent proposal of [Y. Zhang et al. Phys. Rev. B 85, 235151 (2012)], a rotation on the torus yields an alternative basis of ground states and, through the computation of overlaps between bases, the modular matrices S and U (containing the mutual and self statistics of the different anyon species) are extracted. As an application, we study the hard-core boson Haldane model by using the two-dimensional density matrix renormalization group. A thorough characterization of the universal properties of this lattice model, both in the bulk and at the edge, unambiguously shows that its ground space realizes the \nu=1/2 bosonic Laughlin state.Comment: 10 pages, 11 figure