Related papers: Umbilic Lines in Orientational Order
Topological order in two-dimensional systems is studied by combining the braid group formalism with a gauge invariance analysis. We show that flux insertions (or large gauge transformations) pertinent to the toroidal topology induce…
The directed network model describing chiral edge states on the surface of a cylindrical 3D quantum Hall system is known to map to a one-dimensional quantum ferromagnetic spin chain. Using the spin wave expansion for this chain, we…
The fundamental chiral nature of the observed quarks and leptons and the emergence of the gauge group itself are most puzzling aspects of the standard model. Starting from general considerations of topological properties of gauge field…
Causal fermion systems and Riemannian fermion systems are proposed as a framework for describing non-smooth geometries. In particular, this framework provides a setting for spinors on singular spaces. The underlying topological structures…
X-ray tomography is performed to acquire 3D images of crumpled aluminum foils. We develop an algorithm to trace out the labyrinthian paths in the three perpendicular cross sections of the data matrices. The tangent-tangent correlation…
We study automorphism groups of fibered surfaces for finite cyclic covering fibrations of an elliptic surface. We estimate the order of a finite subgroup of automorphism groups in terms of the genus of the fiber, the genus of the base…
Many physical systems involve two types of orientational order, which are coupled together. For example, ferroelectric nematic liquid crystals have coupled polar and nematic order, and tilted hexatic phases have coupled polar and hexatic…
In this paper is studied the behavior of principal curvature lines near a curve of umbilic points of a smooth surface.
We use sets of trivial line bundles for the realization of gerbes. For 1-gerbes the structure arises naturally for the Weyl fermion vacuum bundle at a fixed time. The Schwinger term is an obstruction in the triviality of a 1-gerbe.
In this work we manifest that an electrostatic disorder in conducting systems with broken time reversal symmetry universally leads to a chiral ordering of the electron gas giving rise to skyrmion-like textures in spatial distribution of the…
We introduce topological phases of matter defined by skyrmions in the ground state spin -- or pseudospin -- expectation value textures in the Brillouin zone, the chiral and helical topological skyrmion phases of matter. These phases are…
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…
In this paper is studied the behavior of lines of curvature near umbilic points that appear generically on surfaces depending on two parameters.
For 2D Hubbard model with spin-orbit Rashba coupling in external magnetic field the structure of effective spin interactions is studied in the regime of strong electron correlations and at half-filling. It is shown that in the third order…
Scheme-theoretic methods are used to classify ternary quadratic forms with values in line bundles over arbitrary schemes and to canonically determine the isomorphisms between them. The association of a quadratic bundle to its even Clifford…
Curve singularities are classical objects of study in algebraic geometry. The key player in their combinatorial structure is the {\it value semigroup}, or its compactification, the {\it value semiring}. One natural problem is to explicitly…
We discuss the bifurcation structure of homoclinic orbits in bimodal one dimensional maps. The universal structure of these bifurcations with singular bifurcation points and the web of bifurcation lines through the parameter space are…
The orbital symmetry of the superconducting order parameter in UPt_3 is identified by evaluating the directionally dependent thermalconductivity and ultrasound attenuation in the clean limit and compared with the existing data for both…
The textures associated with a point defect centered in a circular domain of a thin film with XY-like ordering have been analyzed. The family of equilibrium textures, both stable and metastable, can be classified by a new radial topological…
When a ribbon or tube is twisted far enough it forms buckles and wrinkles. Its new geometry can be strikingly ordered, or hopelessly disordered. Here we study this process in a tube with hybrid boundary conditions: one end a cylinder, and…