arXiv subjects

R. Giambò

Publications and source records attributed to R. Giambò.

10 recordsLinked to original sources

arXiv2018

Electronic properties of curved few-layers graphene: a geometrical approach

We show the presence of non-relativistic Lévy-Leblond fermions in flat three- and four-layers graphene with AB stacking, extending the results obtained in [Curvatronics2017] for bilayer graphene. When the layer is curved we obtain a set of equations for Galilean fermions that are a variation of those of Lévy-Leblond with a well defined combination of pseudospin, and that admit Lévy-Leblond spinors as solutions in an approriate limit. The local energy of such Galilean fermions is sensitive to the intrinsic curvature of the surface. We discuss the relationship between two-dimensional pseudospin, labelling layer degrees of freedom, and the different energy bands. For Lévy-Leblond fermions an interpretation is given in terms of massless fermions in an effective 4D spacetime, and in this case the pseudospin is related to four dimensional chirality. A non-zero energy band gap between conduction and valence electronic bands is obtained for surfaces with positive curvature.

cond-mat.mes-hall↗

arXiv2017

Curvatronics with bilayer graphene in an effective $4D$ spacetime

We show that in AB stacked bilayer graphene low energy excitations around the semimetallic points are described by massless, four dimensional Dirac fermions. There is an effective reconstruction of the 4 dimensional spacetime, including in particular the dimension perpendicular to the sheet, that arises dynamically from the physical graphene sheet and the interactions experienced by the carriers. The effective spacetime is the Eisenhart-Duval lift of the dynamics experienced by Galilei invariant Lévy-Leblond spin $\frac{1}{2}$ particles near the Dirac points. We find that changing the intrinsic curvature of the bilayer sheet induces a change in the energy level of the electronic bands, switching from a conducting regime for negative curvature to an insulating one when curvature is positive. In particular, curving graphene bilayers allows opening or closing the energy gap between conduction and valence bands, a key effect for electronic devices. Thus using curvature as a tunable parameter opens the way for the beginning of curvatronics in bilayer graphene.

cond-mat.mes-hall↗

arXiv2015

Functions on the sphere with critical points in pairs and orthogonal geodesic chords

Using an estimate on the number of critical points for a Morse-even function on the sphere $\mathbb S^m$, $m\ge1$, we prove a multiplicity result for orthogonal geodesic chords in Riemannian manifolds with boundary that are diffeomorphic to Euclidean balls. This yields also a multiplicity result for brake orbits in a potential well.

math.DS↗

arXiv2015

On the normal exponential map in singular conformal metrics

Brake orbits and homoclinics of autonomous dynamical systems correspond, via Maupertuis principle, to geodesics in Riemannian manifolds endowed with a metric which is singular on the boundary (Jacobi metric). Motivated by the classical, yet still intriguing in many aspects, problem of establishing multiplicity results for brake orbits and homoclinics, as done in [6, 7, 10], and by the development of a Morse theory in [8] for geodesics in such kind of metric, in this paper we study the related normal exponential map from a global perspective.

math.DS↗

arXiv2015

Multiple brake orbits in $\mathbf m$-dimensional disks

Let $(M,g)$ be a (complete) Riemannian surface, and let $Ω\subset M$ be an open subset whose closure is homeomorphic to a disk. We prove that if $\partialΩ$ is smooth and it satisfies a strong concavity assumption, then there are at least two distinct orthogonal geodesics in $\overlineΩ=Ω\bigcup\partialΩ$. Using the results given in [6], we then obtain a proof of the existence of two distinct brake orbits for a class of Hamiltonian systems. In our proof we shall use recent deformation results proved in [7].

math.DS↗

arXiv2014

Morse Theory for geodesics in singular conformal metrics

Motivated by the use of degenerate Jacobi metrics for the study of brake orbits and homoclinics, we develop a Morse theory for geodesics in conformal metrics having conformal factors vanishing on a regular hypersurface of a Riemannian manifold.

math.DS↗

arXiv2014

Examples with minimal number of brake orbits and homoclinics in annular potential regions

We use a geometric construction to exhibit examples of autonomous Lagrangian systems admitting exactly two homoclinics emanating from a nondegenerate maximum of the potential energy and reaching a regular level of the potential having the same value of the maximum point. Similarly, we show examples of Hamiltonian systems that admit exactly two brake orbits in an annular potential region connecting the two connected components of the boundary of the potential well. These examples show that the estimates proven in [R. Giambò, F. Giannoni, P. Piccione, Arch. Ration. Mech. Anal. 200, (2011) 691-724] are sharp.

math.DS↗

arXiv2012

Collapse of spherical charged anisotropic fluid spacetimes

A class of spherical collapsing exact solutions with electromagnetic charge is derived. This class of solutions -- in general anisotropic -- contains however as a particular case the charged dust model already known in literature. Under some regularity assumptions that in the uncharged case give rise to naked singularities, it is shown that the process of shell focusing singularities avoidance -- already known for the dust collapse -- also takes place here, determing shell crossing effects or a completely regular solution.

gr-qc↗

arXiv2012

Potential wells with a unique brake orbit. Counterexamples to a conjecture by H. Seifert

In this paper we prove the existence of real-analytic natural Hamiltonian systems - i.e. where H(q,p)=T(q,p)+V(q) in the 2N-dimensional real space, where N is any integer greater than 1 - with non critical energy levels E for the potential V such that the sublevel E of V is homeomorphic to the N-dimensional disk, and that only one brake orbit of energy E exists. A famous conjecture formulated by H. Seifert in 1948 claimed the existence of at least N distinct brake orbits for this situation.

math.DS↗

arXiv2007

Dynamics of homogeneous scalar fields with general self-interaction potentials: cosmological and gravitational collapse models

The general relativistic dynamics of a wide class of self-interacting, self-gravitating homogeneous scalar fields models is analyzed. The class is characterized by certain general conditions on the scalar field potential, which include both asymptotically polynomial and exponential behaviors. Within this class, we show that the generic evolution is always divergent in a finite time, and then make use of this result to construct cosmological models as well as radiating collapsing star models of the Vaidya type. It turns out that blackholes are generically formed in such models.

math.CA↗