arXiv subjects

M. Cariglia

Publications and source records attributed to M. Cariglia.

11 recordsLinked to original sources

arXiv2025

Scaling and conformal symmetries for plane gravitational waves

The isometries of an exact plane gravitational wave are symmetries for both massive and massless particles. Their conformal extensions are in fact chrono-projective transformations introduced earlier by Duval et al are symmetries for massless particles. Homotheties are universal chrono-projective symmetries for any profile. Chrono-projective transformations also generate new conserved quantities for the underlying non-relativistic systems in the Bargmann framework. Homotheties play a similar role for the lightlike "vertical" coordinate as isometries play for the transverse coordinates.

gr-qc↗

arXiv2025

Ion Traps and the Memory Effect for Periodic Gravitational Waves

The Eisenhart lift of a Paul Trap used to store ions in molecular physics is a linearly polarized periodic gravitational wave. A modified version of Dehmelt's Penning Trap is in turn related to circularly polarized periodic gravitational waves, sought for in inflationary models. Similar equations rule also the Lagrange points in Celestial Mechanics. The explanation is provided by anisotropic oscillators.

gr-qc↗

arXiv2025

"Kepler Harmonies" and conformal symmetries

Kepler's rescaling becomes, when "Eisenhart-Duval lifted" to $5$-dimensional "Bargmann" gravitational wave spacetime, an ordinary spacetime symmetry for motion along null geodesics, which are the lifts of Keplerian trajectories. The lifted rescaling generates a well-behaved conserved Noether charge upstairs, which takes an unconventional form when expressed in conventional terms. This conserved quantity seems to have escaped attention so far. Applications include the Virial Theorem and also Kepler's Third Law. The lifted Kepler rescaling is a Chrono-Projective transformation. The results extend to celestial mechanics and Newtonian Cosmology.

gr-qc↗

arXiv2018

Lévy-Leblond fermions on the wormhole

We propose a simple model of entanglement generated by geometry, studying non-relativistic massive Lévy-Leblond fermions in the $1+2$ geometry of a Bronnikov-Ellis wormhole. The model is equivalent to that of relativistic massless Dirac fermions in $1+3$ dimensions, where one spatial direction is flat. The effect of the wormhole is to generate quantum states that, far from the throat, are approximated by entangled particles on two flat, separated spacetime regions. An appealing feature of the model is that it has a condensed matter analogue, the regime of intermediate energies for two planes of bilayer graphene linked by a bilayer carbon nanotube. Therefore we expect that it might be possible to realize in the laboratory the entangled states studied here. We argue that generalisations of our solvable model which preserve the topology will have similar quantum behaviour.

gr-qc↗

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↗

arXiv2018

Cosmological aspects of the Eisenhart-Duval lift

A cosmological extension of the Eisenhart-Duval metric is constructed by incorporating a cosmic scale factor and the energy-momentum tensor into the scheme. The dynamics of the spacetime is governed the Ermakov-Milne-Pinney equation. Killing isometries include spatial translations and rotations, Newton--Hooke boosts and translation in the null direction. Geodesic motion in Ermakov-Milne-Pinney cosmoi is analyzed. The derivation of the Ermakov-Lewis invariant, the Friedmann equations and the Dmitriev-Zel'dovich equations within the Eisenhart--Duval framework is presented.

gr-qc↗

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↗

arXiv2016

Eisenhart lifts and symmetries of time-dependent systems

Certain dissipative systems, such as Caldirola and Kannai's damped simple harmonic oscillator, may be modelled by time-dependent Lagrangian and hence time dependent Hamiltonian systems with $n$ degrees of freedom. In this paper we treat these systems, their projective and conformal symmetries as well as their quantisation from the point of view of the Eisenhart lift to a Bargmann spacetime in $n+2$ dimensions, equipped with its covariantly constant null Killing vector field. Reparametrization of the time variable corresponds to conformal rescalings of the Bargmann metric. We show how the Arnold map lifts to Bargmann spacetime. We contrast the greater generality of the Caldirola-Kannai approach with that of Arnold and Bateman. At the level of quantum mechanics, we are able to show how the relevant Schrödinger equation emerges naturally using the techniques of quantum field theory in curved spacetimes, since a covariantly constant null Killing vector field gives rise to well defined one particle Hilbert space. Time-dependent Lagrangians arise naturally also in cosmology and give rise to the phenomenon of Hubble friction. We provide an account of this for Friedmann-Lemaitre and Bianchi cosmologies and how it fits in with our previous discussion in the non-relativistic limit.

hep-th↗

arXiv2014

Conformal Killing Tensors and covariant Hamiltonian Dynamics

A covariant algorithm for deriving the conserved quantities for natural Hamiltonian systems is combined with the non-relativistic framework of Eisenhart, and of Duval, in which the classical trajectories arise as geodesics in a higher dimensional space-time, realized by Brinkmann manifolds. Conserved quantities which are polynomial in the momenta can be built using time-dependent conformal Killing tensors with flux. The latter are associated with terms proportional to the Hamiltonian in the lower dimensional theory and with spectrum generating algebras for higher dimensional quantities of order $1$ and $2$ in the momenta. Illustrations of the general theory include the Runge-Lenz vector for planetary motion with a time-dependent gravitational constant $G(t)$, motion in a time-dependent electromagnetic field of a certain form, quantum dots, the Hénon-Heiles and Holt systems, respectively, providing us with Killing tensors of rank that ranges from one to six.

math-ph↗

arXiv2014

Killing tensors and canonical geometry

The systematic derivation of constants of the motion, based on Killing tensors and the gauge covariant approach, is outlined. Quantum dots are shown to support second-, third- and fourth-rank Killing tensors.

hep-th↗

arXiv2003

Non-Abelian pp-waves in D=4 supergravity theories

The non-Abelian plane waves, first found in flat spacetime by Coleman and subsequently generalized to give pp-waves in Einstein-Yang-Mills theory, are shown to be 1/2 supersymmetric solutions of a wide variety of N=1 supergravity theories coupled to scalar and vector multiplets, including the theory of SU(2) Yang-Mills coupled to an axion σand dilaton ϕrecently obtained as the reduction to four-dimensions of the six-dimensional Salam-Sezgin model. In this latter case they provide the most general supersymmetric solution. Passing to the Riemannian formulation of this theory we show that the most general supersymmetric solution may be constructed starting from a self-dual Yang-Mills connection on a self-dual metric and solving a Poisson equation for e^ϕ. We also present the generalization of these solutions to non-Abelian AdS pp-waves which allow a negative cosmological constant and preserve 1/4 of supersymmetry.

hep-th↗