6,626 research outputs found
Disagreement between correlations of quantum mechanics and stochastic electrodynamics in the damped parametric oscillator
Intracavity and external third order correlations in the damped nondegenerate
parametric oscillator are calculated for quantum mechanics and stochastic
electrodynamics (SED), a semiclassical theory. The two theories yield greatly
different results, with the correlations of quantum mechanics being cubic in
the system's nonlinear coupling constant and those of SED being linear in the
same constant. In particular, differences between the two theories are present
in at least a mesoscopic regime. They also exist when realistic damping is
included. Such differences illustrate distinctions between quantum mechanics
and a hidden variable theory for continuous variables.Comment: accepted by PR
Differential equations for multi-loop integrals and two-dimensional kinematics
In this paper we consider multi-loop integrals appearing in MHV scattering
amplitudes of planar N=4 SYM. Through particular differential operators which
reduce the loop order by one, we present explicit equations for the two-loop
eight-point finite diagrams which relate them to massive hexagons. After the
reduction to two-dimensional kinematics, we solve them using symbol technology.
The terms invisible to the symbols are found through boundary conditions coming
from double soft limits. These equations are valid at all-loop order for double
pentaladders and allow to solve iteratively loop integrals given lower-loop
information. Comments are made about multi-leg and multi-loop integrals which
can appear in this special kinematics. The main motivation of this
investigation is to get a deeper understanding of these tools in this
configuration, as well as for their application in general four-dimensional
kinematics and to less supersymmetric theories.Comment: 25 pages, 7 figure
Spherical Formulation for Diagramatic Evaluations on a Manifold with Boundary
The mathematical formalism necessary for the diagramatic evaluation of
quantum corrections to a conformally invariant field theory for a
self-interacting scalar field on a curved manifold with boundary is considered.
The evaluation of quantum corrections to the effective action past one-loop
necessitates diagramatic techniques. Diagramatic evaluations and higher
loop-order renormalisation can be best accomplished on a Riemannian manifold of
constant curvature accommodating a boundary of constant extrinsic curvature. In
such a context the stated evaluations can be accomplished through a consistent
interpretation of the Feynman rules within the spherical formulation of the
theory for which the method of images allows. To this effect, the mathematical
consequences of such an interpretation are analyzed and the spherical
formulation of the Feynman rules on the bounded manifold is, as a result,
developed.Comment: 12 pages, references added. To appear in Classical and Quantum
Gravit
Yangian symmetry of light-like Wilson loops
We show that a certain class of light-like Wilson loops exhibits a Yangian
symmetry at one loop, or equivalently, in an Abelian theory. The Wilson loops
we discuss are equivalent to one-loop MHV amplitudes in N=4 super Yang-Mills
theory in a certain kinematical regime. The fact that we find a Yangian
symmetry constraining their functional form can be thought of as the effect of
the original conformal symmetry associated to the scattering amplitudes in the
N=4 theory.Comment: 15 pages, 5 figure
Analytic result for the two-loop six-point NMHV amplitude in N=4 super Yang-Mills theory
We provide a simple analytic formula for the two-loop six-point ratio
function of planar N = 4 super Yang-Mills theory. This result extends the
analytic knowledge of multi-loop six-point amplitudes beyond those with maximal
helicity violation. We make a natural ansatz for the symbols of the relevant
functions appearing in the two-loop amplitude, and impose various consistency
conditions, including symmetry, the absence of spurious poles, the correct
collinear behaviour, and agreement with the operator product expansion for
light-like (super) Wilson loops. This information reduces the ansatz to a small
number of relatively simple functions. In order to fix these parameters
uniquely, we utilize an explicit representation of the amplitude in terms of
loop integrals that can be evaluated analytically in various kinematic limits.
The final compact analytic result is expressed in terms of classical
polylogarithms, whose arguments are rational functions of the dual conformal
cross-ratios, plus precisely two functions that are not of this type. One of
the functions, the loop integral \Omega^{(2)}, also plays a key role in a new
representation of the remainder function R_6^{(2)} in the maximally helicity
violating sector. Another interesting feature at two loops is the appearance of
a new (parity odd) \times (parity odd) sector of the amplitude, which is absent
at one loop, and which is uniquely determined in a natural way in terms of the
more familiar (parity even) \times (parity even) part. The second
non-polylogarithmic function, the loop integral \tilde{\Omega}^{(2)},
characterizes this sector. Both \Omega^{(2)} and tilde{\Omega}^{(2)} can be
expressed as one-dimensional integrals over classical polylogarithms with
rational arguments.Comment: 51 pages, 4 figures, one auxiliary file with symbols; v2 minor typo
correction
Real-time model-based slam using line segments
Abstract. Existing monocular vision-based SLAM systems favour interest point features as landmarks, but these are easily occluded and can only be reliably matched over a narrow range of viewpoints. Line segments offer an interesting alternative, as line matching is more stable with respect to viewpoint changes and lines are robust to partial occlusion. In this paper we present a model-based SLAM system that uses 3D line segments as landmarks. Unscented Kalman filters are used to initialise new line segments and generate a 3D wireframe model of the scene that can be tracked with a robust model-based tracking algorithm. Uncertainties in the camera position are fed into the initialisation of new model edges. Results show the system operating in real-time with resilience to partial occlusion. The maps of line segments generated during the SLAM process are physically meaningful and their structure is measured against the true 3D structure of the scene.
The one-loop six-dimensional hexagon integral and its relation to MHV amplitudes in N=4 SYM
We provide an analytic formula for the (rescaled) one-loop scalar hexagon
integral with all external legs massless, in terms of classical
polylogarithms. We show that this integral is closely connected to two
integrals appearing in one- and two-loop amplitudes in planar
super-Yang-Mills theory, and . The derivative of
with respect to one of the conformal invariants yields
, while another first-order differential operator applied to
yields . We also introduce some kinematic
variables that rationalize the arguments of the polylogarithms, making it easy
to verify the latter differential equation. We also give a further example of a
six-dimensional integral relevant for amplitudes in
super-Yang-Mills.Comment: 18 pages, 2 figure
Bayesian total evidence dating reveals the recent crown radiation of penguins
The total-evidence approach to divergence-time dating uses molecular and
morphological data from extant and fossil species to infer phylogenetic
relationships, species divergence times, and macroevolutionary parameters in a
single coherent framework. Current model-based implementations of this approach
lack an appropriate model for the tree describing the diversification and
fossilization process and can produce estimates that lead to erroneous
conclusions. We address this shortcoming by providing a total-evidence method
implemented in a Bayesian framework. This approach uses a mechanistic tree
prior to describe the underlying diversification process that generated the
tree of extant and fossil taxa. Previous attempts to apply the total-evidence
approach have used tree priors that do not account for the possibility that
fossil samples may be direct ancestors of other samples. The fossilized
birth-death (FBD) process explicitly models the diversification, fossilization,
and sampling processes and naturally allows for sampled ancestors. This model
was recently applied to estimate divergence times based on molecular data and
fossil occurrence dates. We incorporate the FBD model and a model of
morphological trait evolution into a Bayesian total-evidence approach to dating
species phylogenies. We apply this method to extant and fossil penguins and
show that the modern penguins radiated much more recently than has been
previously estimated, with the basal divergence in the crown clade occurring at
~12.7 Ma and most splits leading to extant species occurring in the last 2
million years. Our results demonstrate that including stem-fossil diversity can
greatly improve the estimates of the divergence times of crown taxa. The method
is available in BEAST2 (v. 2.4) www.beast2.org with packages SA (v. at least
1.1.4) and morph-models (v. at least 1.0.4).Comment: 50 pages, 6 figure
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