115,019 research outputs found
Charge stripe order from antiphase spin spirals in the spin-Fermion model
We revisit the ground state of the spin-Fermion model within a semiclassical
approximation. We demonstrate that antiphase spin spirals, or pi-spirals, whose
chirality alternates between consecutive rows (or columns) of local moments,
have, for sufficiently high carrier concentration, lower energy than the
traditional Shraiman and Siggia spirals. Furthermore, pi-spirals give rise to
modulated hopping, anisotropic 1D transport, and charge density wave formation.
Finally, we discuss the relevance of pi-spirals to the physics of charge stripe
formation in cuprates, such as La(2-x)Sr(x)CuO4.Comment: 4 pages, 3 figure
Currents and Superpotentials in classical gauge theories: II. Global aspects and the example of Affine gravity
The conserved charges associated with gauge symmetries are defined at a boundary component of spacetime because the corresponding Noether current can be rewritten on-shell as the divergence of a superpotential. However, the latter is afflicted by ambiguities. Regge and Teitelboim found a procedure to lift the arbitrariness in the Hamiltonian framework. An alternative covariant formula was proposed by one of us for an arbitrary variation of the superpotential, it depends only on the equations of motion and on the gauge symmetry under consideration. Here we emphasize that in order to compute the charges, it is enough to stay at a boundary of spacetime, without requiring any hypothesis about the bulk or about other boundary components, so one may speak of holographic charges. It is well known that the asymptotic symmetries that lead to conserved charges are really defined at infinity, but the choice of boundary conditions and surface terms in the action and in the charges is usually determined through integration by parts, whereas each component of the boundary should be considered separately. We treat the example of gravity (for any spacetime dimension, with or without cosmological constant), formulated as an affine theory which is a natural generalization of the Palatini and Cartan-Weyl (vielbein) first-order formulations. We then show that the superpotential associated with a Dirichlet boundary condition on the metric (the one needed to treat asymptotically flat or AdS spacetimes) is the one proposed by Katz et al and not that of Komar. We finally discuss the KBL superpotential at null infinity
On the rotation of ONC stars in the Tsallis formalism context
The theoretical distribution function of the projected rotational velocity is
derived in the context of the Tsallis formalism. The distribution is used to
estimate the average for a stellar sample from the Orion Nebula Cloud
(ONC), producing an excellent result when compared with observational data. In
addition, the value of the parameter q obtained from the distribution of
observed rotations reinforces the idea that there is a relation between this
parameter and the age of the cluster.Comment: 6 pages, 2 figure
Characterization of curves that lie on a geodesic sphere or on a totally geodesic hypersurface in a hyperbolic space or in a sphere
The consideration of the so-called rotation minimizing frames allows for a
simple and elegant characterization of plane and spherical curves in Euclidean
space via a linear equation relating the coefficients that dictate the frame
motion. In this work, we extend these investigations to characterize curves
that lie on a geodesic sphere or totally geodesic hypersurface in a Riemannian
manifold of constant curvature. Using that geodesic spherical curves are normal
curves, i.e., they are the image of an Euclidean spherical curve under the
exponential map, we are able to characterize geodesic spherical curves in
hyperbolic spaces and spheres through a non-homogeneous linear equation.
Finally, we also show that curves on totally geodesic hypersurfaces, which play
the role of hyperplanes in Riemannian geometry, should be characterized by a
homogeneous linear equation. In short, our results give interesting and
significant similarities between hyperbolic, spherical, and Euclidean
geometries.Comment: 15 pages, 3 figures; comments are welcom
Characterization of manifolds of constant curvature by spherical curves
It is known that the so-called rotation minimizing (RM) frames allow for a
simple and elegant characterization of geodesic spherical curves in Euclidean,
hyperbolic, and spherical spaces through a certain linear equation involving
the coefficients that dictate the RM frame motion (da Silva, da Silva in
Mediterr J Math 15:70, 2018). Here, we shall prove the converse, i.e., we show
that if all geodesic spherical curves on a Riemannian manifold are
characterized by a certain linear equation, then all the geodesic spheres with
a sufficiently small radius are totally umbilical and, consequently, the given
manifold has constant sectional curvature. We also furnish two other
characterizations in terms of (i) an inequality involving the mean curvature of
a geodesic sphere and the curvature function of their curves and (ii) the
vanishing of the total torsion of closed spherical curves in the case of
three-dimensional manifolds. Finally, we also show that the same results are
valid for semi-Riemannian manifolds of constant sectional curvature.Comment: To appear in Annali di Matematica Pura ed Applicat
Gaussian Process Structural Equation Models with Latent Variables
In a variety of disciplines such as social sciences, psychology, medicine and
economics, the recorded data are considered to be noisy measurements of latent
variables connected by some causal structure. This corresponds to a family of
graphical models known as the structural equation model with latent variables.
While linear non-Gaussian variants have been well-studied, inference in
nonparametric structural equation models is still underdeveloped. We introduce
a sparse Gaussian process parameterization that defines a non-linear structure
connecting latent variables, unlike common formulations of Gaussian process
latent variable models. The sparse parameterization is given a full Bayesian
treatment without compromising Markov chain Monte Carlo efficiency. We compare
the stability of the sampling procedure and the predictive ability of the model
against the current practice.Comment: 12 pages, 6 figure
Characterization of Spherical and Plane Curves Using Rotation Minimizing Frames
In this work, we study plane and spherical curves in Euclidean and
Lorentz-Minkowski 3-spaces by employing rotation minimizing (RM) frames. By
conveniently writing the curvature and torsion for a curve on a sphere, we show
how to find the angle between the principal normal and an RM vector field for
spherical curves. Later, we characterize plane and spherical curves as curves
whose position vector lies, up to a translation, on a moving plane spanned by
their unit tangent and an RM vector field. Finally, as an application, we
characterize Bertrand curves as curves whose so-called natural mates are
spherical.Comment: 8 pages. This version is an improvement of the previous one. In
addition to a study of some properties of plane and spherical curves, it
contains a characterization of Bertrand curves in terms of the so-called
natural mate
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