46 research outputs found
Curvatronics with bilayer graphene in an effective 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 L\'evy-Leblond spin 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.Comment: 8 pages, 3 figures. Revised version with additional materia
Gravitational collapse of homogeneous scalar fields
Conditions under which gravity coupled to self interacting scalar field
determines singularity formation are found and discussed. It is shown that,
under a suitable matching with an external space, the boundary, if collapses
completely, may give rise to a naked singularity. Issues related to the
strength of the singularity are discussed.Comment: LaTeX2e; revised versio
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.Comment: 10 page
New mathematical framework for spherical gravitational collapse
A theorem, giving necessary and sufficient condition for naked singularity
formation in spherically symmetric non static spacetimes under hypotheses of
physical acceptability, is formulated and proved. The theorem relates existence
of singular null geodesics to existence of regular curves which are
super-solutions of the radial null geodesic equation, and allows us to treat
all the known examples of naked singularities from a unified viewpoint. New
examples are also found using this approach, and perspectives are discussed.Comment: 8 pages, LaTeX2
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.Comment: 13 pages, 2 figures. Version to appear on Class Quantum Gra
Invariant higher-order variational problems II
Motivated by applications in computational anatomy, we consider a
second-order problem in the calculus of variations on object manifolds that are
acted upon by Lie groups of smooth invertible transformations. This problem
leads to solution curves known as Riemannian cubics on object manifolds that
are endowed with normal metrics. The prime examples of such object manifolds
are the symmetric spaces. We characterize the class of cubics on object
manifolds that can be lifted horizontally to cubics on the group of
transformations. Conversely, we show that certain types of non-horizontal
geodesics on the group of transformations project to cubics. Finally, we apply
second-order Lagrange--Poincar\'e reduction to the problem of Riemannian cubics
on the group of transformations. This leads to a reduced form of the equations
that reveals the obstruction for the projection of a cubic on a transformation
group to again be a cubic on its object manifold.Comment: 40 pages, 1 figure. First version -- comments welcome