10,867 research outputs found
A Comparison of the High-Frequency Magnetic Fluctuations in Insulating and Superconducting La2-xSrxCuO4
Inelastic neutron scattering performed at a spallation source is used to make
absolute measurements of the dynamic susceptibility of insulating La2CuO4 and
superconducting La2-xSrxCuO4 over the energy range 15<EN<350 meV. The effect of
Sr doping on the magnetic excitations is to cause a large broadening in
wavevector and a substantial change in the spectrum of the local spin
fluctuations. Comparison of the two compositions reveals a new energy scale of
22 meV in La1.86Sr0.14CuO4.Comment: RevTex, 7 Pages, 4 postscript figure
The Null Decomposition of Conformal Algebras
We analyze the decomposition of the enveloping algebra of the conformal
algebra in arbitrary dimension with respect to the mass-squared operator. It
emerges that the subalgebra that commutes with the mass-squared is generated by
its Poincare subalgebra together with a vector operator. The special cases of
the conformal algebras of two and three dimensions are described in detail,
including the construction of their Casimir operators.Comment: 31 page
Emergence of polarization in a sigmoidal bounded-confidence model of opinion dynamics
We study a nonlinear bounded-confidence model (BCM) of continuous-time
opinion dynamics on networks with both persuadable individuals and zealots. The
model is parameterized by a scalar , which controls the steepness of a
smooth influence function. This influence function encodes the relative weights
that nodes place on the opinions of other nodes. When , this
influence function recovers Taylor's averaging model; when , the influence function converges to that of a modified
Hegselmann--Krause (HK) BCM. Unlike the classical HK model, however, our
sigmoidal bounded-confidence model (SBCM) is smooth for any finite . We
show that the set of steady states of our SBCM is qualitatively similar to that
of the Taylor model when is small and that the set of steady states
approaches a subset of the set of steady states of a modified HK model as
. For several special graph topologies, we give
analytical descriptions of important features of the space of steady states. A
notable result is a closed-form relationship between the stability of a
polarized state and the graph topology in a simple model of echo chambers in
social networks. Because the influence function of our BCM is smooth, we are
able to study it with linear stability analysis, which is difficult to employ
with the usual discontinuous influence functions in BCMs.Comment: 29 pages, 7 figure
Dual conformal constraints and infrared equations from global residue theorems in N=4 SYM theory
Infrared equations and dual conformal constraints arise as consistency
conditions on loop amplitudes in N=4 super Yang-Mills theory. These conditions
are linear relations between leading singularities, which can be computed in
the Grassmannian formulation of N=4 super Yang-Mills theory proposed recently.
Examples for infrared equations have been shown to be implied by global residue
theorems in the Grassmannian picture. Both dual conformal constraints and
infrared equations are mapped explicitly to global residue theorems for
one-loop next-to-maximally-helicity-violating amplitudes. In addition, the
identity relating the BCFW and its parity-conjugated form of tree-level
amplitudes, is shown to emerge from a particular combination of global residue
theorems.Comment: 21 page
Dual Conformal Properties of Six-Dimensional Maximal Super Yang-Mills Amplitudes
We demonstrate that the tree-level amplitudes of maximal super-Yang-Mills
theory in six dimensions, when stripped of their overall momentum and
supermomentum delta functions, are covariant with respect to the
six-dimensional dual conformal group. Using the generalized unitarity method,
we demonstrate that this property is also present for loop amplitudes. Since
the six-dimensional amplitudes can be interpreted as massive four-dimensional
ones, this implies that the six-dimensional symmetry is also present in the
massively regulated four-dimensional maximal super-Yang-Mills amplitudes.Comment: 20 pages, 3 figures, minor clarification, references update
The Soft-Collinear Bootstrap: N=4 Yang-Mills Amplitudes at Six and Seven Loops
Infrared divergences in scattering amplitudes arise when a loop momentum
becomes collinear with a massless external momentum . In gauge
theories, it is known that the L-loop logarithm of a planar amplitude has much
softer infrared singularities than the L-loop amplitude itself. We argue that
planar amplitudes in N=4 super-Yang-Mills theory enjoy softer than expected
behavior as already at the level of the integrand. Moreover,
we conjecture that the four-point integrand can be uniquely determined, to any
loop-order, by imposing the correct soft-behavior of the logarithm together
with dual conformal invariance and dihedral symmetry. We use these simple
criteria to determine explicit formulae for the four-point integrand through
seven-loops, finding perfect agreement with previously known results through
five-loops. As an input to this calculation we enumerate all four-point dual
conformally invariant (DCI) integrands through seven-loops, an analysis which
is aided by several graph-theoretic theorems we prove about general DCI
integrands at arbitrary loop-order. The six- and seven-loop amplitudes receive
non-zero contributions from 229 and 1873 individual DCI diagrams respectively.Comment: 27 pages, 48 figures, detailed results including PDF and Mathematica
files available at http://goo.gl/qIKe8 v2: minor corrections v3: figure 7
corrected, Lemma 2 remove
The ADHM Construction of Instantons on Noncommutative Spaces
We present an account of the ADHM construction of instantons on Euclidean
space-time from the point of view of noncommutative geometry. We
recall the main ingredients of the classical construction in a coordinate
algebra format, which we then deform using a cocycle twisting procedure to
obtain a method for constructing families of instantons on noncommutative
space-time, parameterised by solutions to an appropriate set of ADHM equations.
We illustrate the noncommutative construction in two special cases: the
Moyal-Groenewold plane and the Connes-Landi plane
.Comment: Latex, 40 page
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