arXiv subjects

Marco Cariglia

Publications and source records attributed to Marco Cariglia.

At least 19 recordsLinked to original sources

arXiv2018

General theory of Galilean gravity

We obtain the complete theory of Newton-Cartan gravity in a curved spacetime by considering the large $c$ limit of the vielbein formulation of General Relativity. Milne boosts originate from local Lorentzian transformations, and the special cases of torsionless and twistless torsional geometries are explained in the context of the larger locally Lorentzian theory. We write the action for Newton-Cartan fields in the first order Palatini formalism, and the large $c$ limit of the Einstein equations. Finally, we obtain the generalised Eisenhart-Duval lift of the metric that plays an important role in non-relativistic holography.

gr-qc↗

arXiv2018

On Integrability of the Geodesic Deviation Equation

The Jacobi equation for geodesic deviation describes finite size effects due to the gravitational tidal forces. In this paper we show how one can integrate the Jacobi equation in any spacetime admitting completely integrable geodesics. Namely, by linearizing the geodesic equation and its conserved charges, we arrive at the invariant Wronskians for the Jacobi system that are linear in the `deviation momenta' and thus yield a system of first-order differential equations that can be integrated. The procedure is illustrated on an example of a rotating black hole spacetime described by the Kerr geometry and its higher-dimensional generalizations. A number of related topics, including the phase space formulation of the theory and the derivation of the covariant Hamiltonian for the Jacobi system are also discussed.

gr-qc↗

arXiv2016

Shape-resonant superconductivity in nanofilms: from weak to strong coupling

Ultrathin superconductors of different materials are becoming a powerful platform to find mechanisms for enhancement of superconductivity, exploiting shape resonances in different superconducting properties. Here we evaluate the superconducting gap and its spatial profile, the multiple gap components, and the chemical potential, of generic superconducting nanofilms, considering the pairing attraction and its energy scale as tunable parameters, from weak to strong coupling, at fixed electron density. Superconducting properties are evaluated at mean field level as a function of the thickness of the nanofilm, in order to characterize the shape resonances in the superconducting gap. We find that the most pronounced shape resonances are generated for weakly coupled superconductors, while approaching the strong coupling regime the shape resonances are rounded by a mixing of the subbands due to the large energy gaps extending over large energy scales. Finally, we find that the spatial profile, transverse to the nanofilm, of the superconducting gap acquires a flat behavior in the shape resonance region, indicating that a robust and uniform multigap superconducting state can arise at resonance.

cond-mat.supr-con↗

arXiv2016

Multigap superconductivity and interaction driven resonances in superconducting nanofilms with an inner potential barrier

We study the crossover in a zero temperature superconducting nanofilm from a single to a double superconducting slab induced by a tunable insulating potential barrier in the middle. The single phase superconducting ground state of this heterostructure is shown to be intrinsically multigapped and to have a new type of resonance caused by the strength of the barrier, thus distinct from the Thompson-Blatt shape resonance which is caused by tuning the thickness of the film. Single particle electronic states are strongly or weakly affected according to their parity (even or odd) with respect to the insulating barrier. The lift of the parity degeneracy at finite barrier strength reconfigures the pairing interaction and leads to a multigapped superconducting state with interaction driven resonances.

cond-mat.supr-con↗

arXiv2015

Zero helicity states in the $LaAlO_3/SrTiO_3$ interface

We propose a kinetically driven mechanism based on the breaking of the spatial reflection symmetry to describe the magnetic moment and the torque observed by Lu-Li et al. (Ref. 1) for the $LaAlO_3/SrTiO_3$ system. We find that the itinerant electrons are in a zero helicity state and predict the existence of charge inhomogeneities that cross the interface at constant rate. There is mass and thickness anisotropies between the two sides of the interface.

cond-mat.supr-con↗

arXiv2015

Conformal Triality of the Kepler problem

We show that the Kepler problem is projectively equivalent to null geodesic motion on the conformal compactification of Minkowski-4 space. This space realises the conformal triality of Minkwoski, dS and AdS spaces.

gr-qc↗

arXiv2015

Null lifts and projective dynamics

We describe natural Hamiltonian systems using projective geometry. The null lift procedure endows the tangent bundle with a projective structure where the null Hamiltonian is identified with a projective conic and induces a Weyl geometry. Projective transformations generate a set of known and new dualities between Hamiltonian systems, as for example the phenomenon of coupling-constant metamorphosis. We conclude outlining how this construction can be extended to the quantum case for Eisenhart-Duval lifts.

math-ph↗

arXiv2015

Ricci-flat spacetimes admitting higher rank Killing tensors

Ricci-flat spacetimes of signature (2,q) with q=2,3,4 are constructed which admit irreducible Killing tensors of rank-3 or rank-4. The construction relies upon the Eisenhart lift applied to Drach's two-dimensional integrable systems which is followed by the oxidation with respect to free parameters. In four dimensions, some of our solutions are anti-self-dual.

gr-qc↗

arXiv2015

The Eisenhart lift: a didactical introduction of modern geometrical concepts from Hamiltonian dynamics

This work originates from part of a final year undergraduate research project on the Eisenhart lift for Hamiltonian systems. The Eisenhart lift is a procedure to describe trajectories of a classical natural Hamiltonian system as geodesics in an enlarged space. We point out that it can be easily obtained from basic principles of Hamiltonian dynamics, and as such it represents a useful didactical way to introduce graduate students to several modern concepts of geometry applied to physics: curved spaces, both Riemannian and Lorentzian, conformal transformations, geometrisation of interactions and extra dimensions, geometrisation of dynamical symmetries. For all these concepts the Eisenhart lift can be used as a theoretical tool that provides easily achievable examples, with the added benefit of also being a topic of current research with several applications, among which the study of dynamical systems and non-relativistic holography.

gr-qc↗

arXiv2014

Hidden Symmetries of Dynamics in Classical and Quantum Physics

This article reviews the role of hidden symmetries of dynamics in the study of physical systems, from the basic concepts of symmetries in phase space to the forefront of current research. Such symmetries emerge naturally in the description of physical systems as varied as non-relativistic, relativistic, with or without gravity, classical or quantum, and are related to the existence of conserved quantities of the dynamics and integrability. In recent years their study has grown intensively, due to the discovery of non-trivial examples that apply to different types of theories and different numbers of dimensions. Applications encompass the study of integrable systems such as spinning tops, the Calogero model, systems described by the Lax equation, the physics of higher dimensional black holes, the Dirac equation, supergravity with and without fluxes, providing a tool to probe the dynamics of non-linear systems.

math-ph↗

arXiv2014

Coexistence of magnetic and charge order in a two-component order parameter description of the layered superconductors

A two-component order parameter approach for the layered superconductor is shown to form a condensate with magnetic and charge degrees of freedom. This condensate is an inhomogeneous state, topologically stable, that exists without the presence of an applied magnetic field. We show that the charge density in the layers presents hexadecapole moment in its lowest order. Our approach is based on the first order equations that we show here to solve the variational equations for the special temperature defined by the crossing of the superconducting dome and the pseudogap transition line. Time reversal symmetry is broken and the weak local magnetic field produced by this inhomogeneous state falls below the threshold of experimental observation. We find that the charge distribution in the layers has an hexadecapole moment in its lowest order.

cond-mat.supr-con↗

arXiv2014

Is the pseudogap a topological state?

We conjecture that the pseudogap is an inhomogeneous condensate above the homogeneous state whose existence is granted by topological stability. We consider the simplest possible order parameter theory that provides this interpretation of the pseudogap and study its angular momentum states. The normal state gap density, the breaking of the time reversal symmetry and the checkerboard pattern are naturally explained under this view. The pseudogap is a lattice of skyrmions and the inner weak local magnetic field falls below the experimental threshold of observation given by NMR/NQR and $μ$SR experiments.

cond-mat.supr-con↗

arXiv2013

Generalised Eisenhart lift of the Toda chain

The Toda chain of nearest neighbour interacting particles on a line can be described both in terms of geodesic motion on a manifold with one extra dimension, the Eisenhart lift, or in terms of geodesic motion in a symmetric space with several extra dimensions. We examine the relationship between these two realisations and discover that the symmetric space is a generalised, multi-particle Eisenhart lift of the original problem, that reduces to the standard Eisenhart lift. Such generalised Eisenhart lift acts as an inverse Kaluza-Klein reduction, promoting coupling constants to momenta in higher dimension. In particular, isometries of the generalised lift metric correspond to energy preserving transformations that mix coordinates and coupling constants. A by-product of the analysis is that the lift of the Toda Lax pair can be used to construct higher rank Killing tensors for both the standard and generalised lift metrics.

math-ph↗

arXiv2013

Evidence for skyrmions in the high-temperature superconductors

We claim that the charge density wave recently found by resonant soft x-ray scattering in layered copper oxides is the tetragonal symmetry defined by the distance between neighbor Cu$^{3+}$ ions in the CuO$_2$ layer that determines the critical temperature. We find evidence that this tetragonal symmetry is a skyrmionic state, which is responsible for an unusual magnetic order and charge flow in the layers that leads to the breaking of the time reversal symmetry below the pseudogap line. The core of the skyrmions form pockets of local magnetic field piercing the superconducting layers in opposite direction to the rest of the unit cell.

cond-mat.supr-con↗

arXiv2013

Topologically stable gapped state in a layered superconductor

We show that a layered superconductor, described by a two-component order parameter, has a gapped state above the ground state, topologically protected from decay, containing flow and counter flow in the absence of an applied magnetic field. This state is made of skyrmions, breaks time reversal symmetry and produces a weak local magnetic field below the present threshold of detection by $μ$SR and NMR/NQR. We estimate the density of carriers that condense into the pseudogap.

cond-mat.supr-con↗

arXiv2013

Dynamical symmetries of the Kepler problem

This work originates from a first year undergraduate research project on hidden symmetries of the dynamics for classical Hamiltonian systems, under the program 'Jovens talentos para a Ciencia' of Brazilian funding agency Capes. For pedagogical reasons the main subject chosen was Kepler's problem of motion under a central potential, since it is a completely solved system. It is well known that for this problem the group of dynamical symmetries is strictly larger than the isometry group O(3), the extra symmetries corresponding to hidden symmetries of the dynamics. By taking the point of view of examining the group action of the dynamical symmetries on the allowed trajectories, it is possible to teach in the same project basic elements of as many important subjects in physics as: Hamiltonian formalism, hidden symmetries, integrable systems, group theory, and the use of manifolds.

physics.class-ph↗

arXiv2012

Electron in higher-dimensional weakly charged rotating black hole spacetimes

We demonstrate separability of the Dirac equation in weakly charged rotating black hole spacetimes in all dimensions. The electromagnetic field of the black hole is described by a test field approximation, with vector potential proportional to the primary Killing vector field. It is shown that the demonstrated separability can be intrinsically characterized by the existence of a complete set of mutually commuting first order symmetry operators generated from the principal Killing-Yano tensor. The presented results generalize the results on integrability of charged particle motion and separability of charged scalar field studied in [1].

gr-qc↗

arXiv2012

Geometry of Lax pairs: particle motion and Killing-Yano tensors

A geometric formulation of the Lax pair equation on a curved manifold is studied using phase space formalism. The corresponding (covariantly conserved) Lax tensor is defined and the method of generation of constants of motion from it is discussed. It is shown that when the Hamilton equations of motion are used, the conservation of the Lax tensor translates directly to the well known Lax pair equation, with one matrix identified with components of the Lax tensor and the other matrix constructed from the (metric) connection. A generalization to Clifford objects is also discussed. Nontrivial examples of Lax tensors for geodesic and charged particle motion are found in spacetimes admitting hidden symmetry of Killing--Yano tensors.

math-ph↗