Search results for "Homogeneous space"
showing 10 items of 142 documents
Bifurcations of Links of Periodic Orbits in Non-Singular Systems with Two Rotational Symmetries on S3
1997
A topological characterization of all possible links composed of the periodic orbits of a Non Singular Morse-Smale flow on S3 has been made by M. Wada. The presence of symmetry forces the appearance of given types of links. In this paper we introduce a geometrical tool to represent these type of links when a symmetry around two axes is considered on NMS systems: mosaics. On the other hand, we use mosaics to study what kind of bifurcation can occur in this type of system maintaining the symmetry.
On the derived category of the Cayley plane II
2014
We find a full strongly exceptional collection for the Cayley plane OP2, the simplest rational homogeneous space of the exceptional group E6. This collection, closely related to the one given by the second author in [J. Algebra, 330:177-187, 2011], consists of 27 vector bundles which are homogeneous for the group E6, and is a Lefschetz collection with respect to the minimal equivariant embedding of OP2.
Symmetries in Spaces, Symmetries in Listening
2018
Based on the importance of the concept of symmetry in French sociological aesthetics circa 1900, this chapter analyzes the convergence of theaters, musical form, and musical understanding. The analysis focuses on architectural shape, audience response, and the musical repertoire in the new theaters built in Barcelona (1847), Paris (1862), and Rome (1880). While these theaters were fashioned after the baroque form of the “teatro all’italiana” that prevailed in Italy, France, and Spain during the late nineteenth century, they provided huge spaces accommodating a socially mixed audience within an architecturally symmetrical form. Music critics often aligned acoustic sound waves with actual vis…
Regularization of spherical and axisymmetric evolution codes in numerical relativity
2007
Several interesting astrophysical phenomena are symmetric with respect to the rotation axis, like the head-on collision of compact bodies, the collapse and/or accretion of fields with a large variety of geometries, or some forms of gravitational waves. Most current numerical relativity codes, however, can not take advantage of these symmetries due to the fact that singularities in the adapted coordinates, either at the origin or at the axis of symmetry, rapidly cause the simulation to crash. Because of this regularity problem it has become common practice to use full-blown Cartesian three-dimensional codes to simulate axi-symmetric systems. In this work we follow a recent idea idea of Rinne…
Effect of three-body forces on response functions in infinite neutron matter
2015
International audience; We study the impact of three-body forces on the response functions of cold neutron matter. These response functions are determined in the random phase approximation (RPA) from a residual interaction expressed in terms of Landau parameters. Special attention is paid to the non-central part, including all terms allowed by the relevant symmetries. Using Landau parameters derived from realistic nuclear two- and three-body forces grounded in chiral effective field theory, we find that the three-body term has a strong impact on the excited states of the system and in the static and long-wavelength limit of the response functions for which a new exact formula is established.
Gδ covers of compact spaces
2018
We solve a long standing question due to Arhangel'skii by constructing a compact space which has a Gδ cover with no continuum-sized (Gδ)-dense subcollection. We also prove that in a countably compact weakly Lindelöf normal space of countable tightness, every Gδ cover has a -sized subcollection with a Gδ-dense union and that in a Lindelöf space with a base of multiplicity continuum, every Gδ cover has a continuum sized subcover. We finally apply our results to obtain a bound on the cardinality of homogeneous spaces which refines De La Vega's celebrated theorem on the cardinality of homogeneous compacta of countable tightness.
Electromagnetic transitions of heavy baryons in theSU(2Nf)⊗O(3)symmetry
2001
We apply heavy quark symmetry to the radiative decays of heavy baryons. Even with this symmetry in place there are too many couplings to make a meaningful set of predictions. We show that if, in addition, light-diquark symmetries are applied, the number of electromagnetic couplings among S wave and P wave states as well as those between P wave to S wave transitions can be reduced significantly. Using this constituent quark model picture a number of predictions are made that will be testable in the near future.
Chiral expansion of the nucleon mass to order q^6
2006
We present the results of a complete two-loop calculation at order q^6 of the nucleon mass in manifestly Lorentz-invariant chiral perturbation theory. The renormalization is performed using the reformulated infrared renormalization, which allows for the treatment of two-loop integrals while preserving all relevant symmetries, in particular chiral symmetry.
Chiralities of nodal points along high symmetry lines with screw rotation symmetry
2021
Screw rotations in nonsymmorphic space group symmetries induce the presence of hourglass and accordion shape band structures along screw invariant lines whenever spin-orbit coupling is nonnegligible. These structures induce topological enforced Weyl points on the band intersections. In this work we show that the chirality of each Weyl point is related to the representations of the cyclic group on the bands that form the intersection. To achieve this, we calculate the Picard group of isomorphism classes of complex line bundles over the 2-dimensional sphere with cyclic group action, and we show how the chirality (Chern number) relates to the eigenvalues of the rotation action on the rotation …
Breaking of SU(4) symmetry and interplay between strongly correlated phases in the Hubbard model
2016
We study the thermodynamic properties of four-component fermionic mixtures described by the Hubbard model using the dynamical mean-field-theory approach. Special attention is given to the system with SU(4)-symmetric interactions at half filling, where we analyze equilibrium many-body phases and their coexistence regions at nonzero temperature for the case of simple cubic lattice geometry. We also determine the evolution of observables in low-temperature phases while lowering the symmetry of the Hamiltonian towards the two-band Hubbard model. This is achieved by varying interflavor interactions or by introducing the spin-flip term (Hund's coupling). By calculating the entropy for different s…