25,916 research outputs found
Isotrivial VMRT-structures of complete intersection type
The family of varieties of minimal rational tangents on a quasi-homogeneous
projective manifold is isotrivial. Conversely, are projective manifolds with
isotrivial varieties of minimal rational tangents quasi-homogenous? We will
show that this is not true in general, even when the projective manifold has
Picard number 1. In fact, an isotrivial family of varieties of minimal rational
tangents needs not be locally flat in differential geometric sense. This leads
to the question for which projective variety Z, the Z-isotriviality of
varieties of minimal rational tangents implies local flatness. Our main result
verifies this for many cases of Z among complete intersections.Comment: Some errors in Section 8 and Lemma 8.1 corrected. To appear in The
Asian Journal of Mathematics (AJM) special issue dedicated to Ngaiming Mok's
60th birthda
Cosmological perturbations in a gravity with quadratic order curvature couplings
We present a set of equations describing the evolution of the scalar-type
cosmological perturbation in a gravity with general quadratic order curvature
coupling terms. Equations are presented in a gauge ready form, thus are ready
to implement various temporal gauge conditions depending on the problems. The
Ricci-curvature square term leads to a fourth-order differential equation for
describing the spacetime fluctuations in a spatially homogeneous and isotropic
cosmological background.Comment: 5 pages, no figure, To appear in Phys. Rev.
Quantum fluctuations of Cosmological Perturbations in Generalized Gravity
Recently, we presented a unified way of analysing classical cosmological
perturbation in generalized gravity theories. In this paper, we derive the
perturbation spectrums generated from quantum fluctuations again in unified
forms. We consider a situation where an accelerated expansion phase of the
early universe is realized in a particular generic phase of the generalized
gravity. We take the perturbative semiclassical approximation which treats the
perturbed parts of the metric and matter fields as quantum mechanical
operators. Our generic results include the conventional power-law and
exponential inflations in Einstein's gravity as special cases.Comment: 5 pages, revtex, no figure
Conserved cosmological structures in the one-loop superstring effective action
A generic form of low-energy effective action of superstring theories with
one-loop quantum correction is well known. Based on this action we derive the
complete perturbation equations and general analytic solutions in the
cosmological spacetime. Using the solutions we identify conserved quantities
characterizing the perturbations: the amplitude of gravitational wave and the
perturbed three-space curvature in the uniform-field gauge both in the
large-scale limit, and the angular-momentum of rotational perturbation are
conserved independently of changing gravity sector. Implications for
calculating perturbation spectra generated in the inflation era based on the
string action are presented.Comment: 5 pages, no figure, To appear in Phys. Rev.
Unified Analysis of Cosmological Perturbations in Generalized Gravity
In a class of generalized Einstein's gravity theories we derive the equations
and general asymptotic solutions describing the evolution of the perturbed
universe in unified forms. Our gravity theory considers general couplings
between the scalar field and the scalar curvature in the Lagrangian, thus
includes broad classes of generalized gravity theories resulting from recent
attempts for the unification. We analyze both the scalar-type mode and the
gravitational wave in analogous ways. For both modes the large scale evolutions
are characterized by the same conserved quantities which are valid in the
Einstein's gravity. This unified and simple treatment is possible due to our
proper choice of the gauges, or equivalently gauge invariant combinations.Comment: 4 pages, revtex, no figure
Relativistic Hydrodynamic Cosmological Perturbations
Relativistic cosmological perturbation analyses can be made based on several
different fundamental gauge conditions. In the pressureless limit the variables
in certain gauge conditions show the correct Newtonian behaviors. Considering
the general curvature () and the cosmological constant () in the
background medium, the perturbed density in the comoving gauge, and the
perturbed velocity and the perturbed potential in the zero-shear gauge show the
same behavior as the Newtonian ones in general scales. In the first part, we
elaborate these Newtonian correspondences. In the second part, using the
identified gauge-invariant variables with correct Newtonian correspondences, we
present the relativistic results with general pressures in the background and
perturbation. We present the general super-sound-horizon scale solutions of the
above mentioned variables valid for general , , and generally
evolving equation of state. We show that, for vanishing , the
super-sound-horizon scale evolution is characterised by a conserved variable
which is the perturbed three-space curvature in the comoving gauge. We also
present equations for the multi-component hydrodynamic situation and for the
rotation and gravitational wave.Comment: 16 pages, no figure, To appear in Gen. Rel. Gra
Origin of the mixed-order transition in multiplex networks: the Ashkin-Teller model
Recently, diverse phase transition (PT) types have been obtained in multiplex
networks, such as discontinuous, continuous, and mixed-order PTs. However, they
emerge from individual systems, and there is no theoretical understanding of
such PTs in a single framework. Here, we study a spin model called the
Ashkin-Teller (AT) model in a mono-layer scale-free network; this can be
regarded as a model of two species of Ising spin placed on each layer of a
double-layer network. The four-spin interaction in the AT model represents the
inter-layer interaction in the multiplex network. Diverse PTs emerge depending
on the inter-layer coupling strength and network structure. Especially, we find
that mixed-order PTs occur at the critical end points. The origin of such
behavior is explained in the framework of Landau-Ginzburg theory.Comment: 10 pages, 5 figure
Electron-boson spectral density of LiFeAs obtained from optical data
We analyze existing optical data in the superconducting state of LiFeAs at 4 K, to recover its electron-boson spectral density. A maximum entropy
technique is employed to extract the spectral density from
the optical scattering rate. Care is taken to properly account for elastic
impurity scattering which can importantly affect the optics in an -wave
superconductor, but does not eliminate the boson structure. We find a robust
peak in centered about 8.0 meV or 5.3 (with 17.6 K). Its position in energy agrees well with a similar
structure seen in scanning tunneling spectroscopy (STS). There is also a peak
in the inelastic neutron scattering (INS) data at this same energy. This peak
is found to persist in the normal state at 23 K. There is evidence that
the superconducting gap is anisotropic as was also found in low temperature
angular resolved photoemission (ARPES) data.Comment: 17 pages, 6 figure
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