9,342 research outputs found
A new dawn? The Roman Catholic Church and environmental issues
This is a PDF version of an article published in New Blackfriars© 1997. The definitive version is available at www.blackwell-synergy.com.This article discusses the stance of the Roman Catholic Church on environmental issues and argues that the Church tends to stay on the fringe rather than get involved. Some of the ways in which Roman Catholic theologians have incorporated environmental issues into theological reflection is discussed, as are environmental challenges facing the Church in Britain (conservation, resources, biodiversity, animal welfare, biotechnology, cooperate/individual ethics, environmental justice, economics/policy development, and global issues)
First-principles quantum dynamics in interacting Bose gases I: The positive P representation
The performance of the positive P phase-space representation for exact
many-body quantum dynamics is investigated. Gases of interacting bosons are
considered, where the full quantum equations to simulate are of a
Gross-Pitaevskii form with added Gaussian noise. This method gives tractable
simulations of many-body systems because the number of variables scales
linearly with the spatial lattice size. An expression for the useful simulation
time is obtained, and checked in numerical simulations. The dynamics of first-,
second- and third-order spatial correlations are calculated for a uniform
interacting 1D Bose gas subjected to a change in scattering length. Propagation
of correlations is seen. A comparison is made to other recent methods. The
positive P method is particularly well suited to open systems as no
conservation laws are hard-wired into the calculation. It also differs from
most other recent approaches in that there is no truncation of any kind.Comment: 21 pages, 7 figures, 2 tables, IOP styl
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
Tree-Level Amplitudes in N=8 Supergravity
We present an algorithm for writing down explicit formulas for all tree
amplitudes in N=8 supergravity, obtained from solving the supersymmetric
on-shell recursion relations. The formula is patterned after one recently
obtained for all tree amplitudes in N=4 super Yang-Mills which involves nested
sums of dual superconformal invariants. We find that all graviton amplitudes
can be written in terms of exactly the same structure of nested sums with two
modifications: the dual superconformal invariants are promoted from N=4 to N=8
superspace in the simplest manner possible--by squaring them--and certain
additional non-dual conformal gravity dressing factors (independent of the
superspace coordinates) are inserted into the nested sums. To illustrate the
procedure we give explicit closed-form formulas for all NMHV, NNMHV and NNNMV
gravity superamplitudes.Comment: 27 pages, 5 figures, v2: typos correcte
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
The time-reversal test for stochastic quantum dynamics
The calculation of quantum dynamics is currently a central issue in
theoretical physics, with diverse applications ranging from ultra-cold atomic
Bose-Einstein condensates (BEC) to condensed matter, biology, and even
astrophysics. Here we demonstrate a conceptually simple method of determining
the regime of validity of stochastic simulations of unitary quantum dynamics by
employing a time-reversal test. We apply this test to a simulation of the
evolution of a quantum anharmonic oscillator with up to
(Avogadro's number) of particles. This system is realisable as a Bose-Einstein
condensate in an optical lattice, for which the time-reversal procedure could
be implemented experimentally.Comment: revtex4, two figures, four page
Relating Superembeddings and Non-linear Realisations
We discuss the relation between the superembedding method for deriving
worldvolume actions for D-branes and the method of Partially Broken Global
Supersymmetry based upon linear and non-linear realisations of SUSY. We give
the explicit relation for the cases of space filling branes in 3 and 4
dimensions and show that the standard F-constraint of the superembedding method
is the source of the required covariant non-linear constraints for the PBGS
method.Comment: 19 pages. Improved spelling, references adde
On the Classification of Residues of the Grassmannian
We study leading singularities of scattering amplitudes which are obtained as
residues of an integral over a Grassmannian manifold. We recursively do the
transformation from twistors to momentum twistors and obtain an iterative
formula for Yangian invariants that involves a succession of dualized twistor
variables. This turns out to be useful in addressing the problem of classifying
the residues of the Grassmannian. The iterative formula leads naturally to new
coordinates on the Grassmannian in terms of which both composite and
non-composite residues appear on an equal footing. We write down residue
theorems in these new variables and classify the independent residues for some
simple examples. These variables also explicitly exhibit the distinct solutions
one expects to find for a given set of vanishing minors from Schubert calculus.Comment: 20 page
Naturally-phasematched second harmonic generation in a whispering gallery mode resonator
We demonstrate for the first time natural phase matching for optical
frequency doubling in a high-Q whispering gallery mode resonator made of
Lithium Niobate. A conversion efficiency of 9% is achieved at 30 micro Watt
in-coupled continuous wave pump power. The observed saturation pump power of
3.2 mW is almost two orders of magnitude lower than the state-of-the-art. This
suggests an application of our frequency doubler as a source of non-classical
light requiring only a low-power pump, which easily can be quantum noise
limited. Our theoretical analysis of the three-wave mixing in a whispering
gallery mode resonator provides the relative conversion efficiencies for
frequency doubling in various modes
Gaussian phase-space representations for fermions
We introduce a positive phase-space representation for fermions, using the
most general possible multi-mode Gaussian operator basis. The representation
generalizes previous bosonic quantum phase-space methods to Fermi systems. We
derive equivalences between quantum and stochastic moments, as well as operator
correspondences that map quantum operator evolution onto stochastic processes
in phase space. The representation thus enables first-principles quantum
dynamical or equilibrium calculations in many-body Fermi systems. Potential
applications are to strongly interacting and correlated Fermi gases, including
coherent behaviour in open systems and nanostructures described by master
equations. Examples of an ideal gas and the Hubbard model are given, as well as
a generic open system, in order to illustrate these ideas.Comment: More references and examples. Much less mathematical materia
- …