41,402 research outputs found
Spherical geometry and integrable systems
We prove that the cosine law for spherical triangles and spherical tetrahedra
defines integrable systems, both in the sense of multidimensional consistency
and in the sense of dynamical systems.Comment: 15 pages, 5 figure
Scalar diagrammatic rules for Born amplitudes in QCD
We show that all Born amplitudes in QCD can be calculated from scalar
propagators and a set of three- and four-valent vertices. In particular, our
approach includes amplitudes with any number of quark pairs. The quarks may be
massless or massive. The proof of the formalism is given entirely within
quantum field theory.Comment: 20 pages, references adde
Orbital and interlayer Skyrmions crystals in bilayer graphene
A graphene bilayer in a transverse magnetic field has a set of Landau levels
with energies where
is the effective cyclotron frequency and
All Landau levels but N=0 are four times degenerate counting spin and valley
degrees of freedom. The Landau level N=0 has an extra degeneracy due to the
fact that orbitals and both have zero kinetic energies. At integer
filling factors, Coulomb interactions produce a set of broken-symmetry states
with partial or full alignement in space of the valley and orbital pseudospins.
These quantum Hall pseudo-ferromagnetic states support topological charged
excitations in the form of orbital and valley Skyrmions. Away from integer
fillings, these topological excitations can condense to form a rich variety of
Skyrme crystals with interesting properties. We study in this paper different
crystal phases that occur when an electric field is applied between the layers.
We show that orbital Skyrmions, in analogy with spin Skyrmions, have a texture
of electrical dipoles that can be controlled by an in-plane electric field.
Moreover, the modulation of electronic density in the crystalline phases are
experimentally accessible through a measurement of their local density of
statesComment: 18 pages with 13 figure
Bound States and Critical Behavior of the Yukawa Potential
We investigate the bound states of the Yukawa potential , using different algorithms: solving the Schr\"odinger
equation numerically and our Monte Carlo Hamiltonian approach. There is a
critical , above which no bound state exists. We study the
relation between and for various angular momentum quantum
number , and find in atomic units, , with , ,
, and .Comment: 15 pages, 12 figures, 5 tables. Version to appear in Sciences in
China
Seeding for pervasively overlapping communities
In some social and biological networks, the majority of nodes belong to
multiple communities. It has recently been shown that a number of the
algorithms that are designed to detect overlapping communities do not perform
well in such highly overlapping settings. Here, we consider one class of these
algorithms, those which optimize a local fitness measure, typically by using a
greedy heuristic to expand a seed into a community. We perform synthetic
benchmarks which indicate that an appropriate seeding strategy becomes
increasingly important as the extent of community overlap increases. We find
that distinct cliques provide the best seeds. We find further support for this
seeding strategy with benchmarks on a Facebook network and the yeast
interactome.Comment: 8 Page
One-Loop MHV Amplitudes in Supersymmetric Gauge Theories
Using CSW rules for constructing scalar Feynman diagrams from MHV vertices,
we compute the contribution of chiral multiplet to one-loop
MHV gluon amplitude. The result agrees with the one obtained previously using
unitarity-based methods, thereby demonstrating the validity of the MHV-diagram
technique, in the case of one-loop MHV amplitudes, for all massless
supersymmetric theories.Comment: 20 pages, 5 figure
- …