94,895 research outputs found
Quantum Cosmological Relational Model of Shape and Scale in 1-d
Relational particle models are useful toy models for quantum cosmology and
the problem of time in quantum general relativity. This paper shows how to
extend existing work on concrete examples of relational particle models in 1-d
to include a notion of scale. This is useful as regards forming a tight analogy
with quantum cosmology and the emergent semiclassical time and hidden time
approaches to the problem of time. This paper shows furthermore that the
correspondence between relational particle models and classical and quantum
cosmology can be strengthened using judicious choices of the mechanical
potential. This gives relational particle mechanics models with analogues of
spatial curvature, cosmological constant, dust and radiation terms. A number of
these models are then tractable at the quantum level. These models can be used
to study important issues 1) in canonical quantum gravity: the problem of time,
the semiclassical approach to it and timeless approaches to it (such as the
naive Schrodinger interpretation and records theory). 2) In quantum cosmology,
such as in the investigation of uniform states, robustness, and the qualitative
understanding of the origin of structure formation.Comment: References and some more motivation adde
Atomic-phase interference devices based on ring-shaped Bose-Einstein condensates: Two ring case
We theoretically investigate the ground-state properties and quantum dynamics
of a pair of adjacent ring-shaped Bose-Einstein condensates that are coupled
via tunneling. This device, which is the analogue of a symmetric
superconducting quantum interference device, is the simplest version of what we
term an Atomic-Phase Interference Device (APHID). The two-ring APHID is shown
to be sensitive to rotation.Comment: 8 page
New interpretation of variational principles for gauge theories. I. Cyclic coordinate alternative to ADM split
I show how there is an ambiguity in how one treats auxiliary variables in
gauge theories including general relativity cast as 3 + 1 geometrodynamics.
Auxiliary variables may be treated pre-variationally as multiplier coordinates
or as the velocities corresponding to cyclic coordinates. The latter treatment
works through the physical meaninglessness of auxiliary variables' values
applying also to the end points (or end spatial hypersurfaces) of the
variation, so that these are free rather than fixed. [This is also known as
variation with natural boundary conditions.] Further principles of dynamics
workings such as Routhian reduction and the Dirac procedure are shown to have
parallel counterparts for this new formalism. One advantage of the new scheme
is that the corresponding actions are more manifestly relational. While the
electric potential is usually regarded as a multiplier coordinate and Arnowitt,
Deser and Misner have regarded the lapse and shift likewise, this paper's
scheme considers new {\it flux}, {\it instant} and {\it grid} variables whose
corresponding velocities are, respectively, the abovementioned previously used
variables. This paper's way of thinking about gauge theory furthermore admits
interesting generalizations, which shall be provided in a second paper.Comment: 11 page
Approaching the Problem of Time with a Combined Semiclassical-Records-Histories Scheme
I approach the Problem of Time and other foundations of Quantum Cosmology
using a combined histories, timeless and semiclassical approach. This approach
is along the lines pursued by Halliwell. It involves the timeless probabilities
for dynamical trajectories entering regions of configuration space, which are
computed within the semiclassical regime. Moreover, the objects that Halliwell
uses in this approach commute with the Hamiltonian constraint, H. This approach
has not hitherto been considered for models that also possess nontrivial linear
constraints, Lin. This paper carries this out for some concrete relational
particle models (RPM's). If there is also commutation with Lin - the Kuchar
observables condition - the constructed objects are Dirac observables.
Moreover, this paper shows that the problem of Kuchar observables is explicitly
resolved for 1- and 2-d RPM's. Then as a first route to Halliwell's approach
for nontrivial linear constraints that is also a construction of Dirac
observables, I consider theories for which Kuchar observables are formally
known, giving the relational triangle as an example. As a second route, I apply
an indirect method that generalizes both group-averaging and Barbour's best
matching. For conceptual clarity, my study involves the simpler case of
Halliwell 2003 sharp-edged window function. I leave the elsewise-improved
softened case of Halliwell 2009 for a subsequent Paper II. Finally, I provide
comments on Halliwell's approach and how well it fares as regards the various
facets of the Problem of Time and as an implementation of QM propositions.Comment: An improved version of the text, and with various further references.
25 pages, 4 figure
The Final Remnant of Binary Black Hole Mergers: Multipolar Analysis
Methods are presented to define and compute source multipoles of dynamical
horizons in numerical relativity codes, extending previous work from the
isolated and dynamical horizon formalisms in a manner that allows for the
consideration of horizons that are not axisymmetric. These methods are then
applied to a binary black hole merger simulation, providing evidence that the
final remnant is a Kerr black hole, both through the (spatially)
gauge-invariant recovery of the geometry of the apparent horizon, and through a
detailed extraction of quasinormal ringing modes directly from the strong-field
region.Comment: 12 pages, 13 figures. Published version. Some references have been
added and reordered, and the figures cleaned up
Deterministic creation, pinning, and manipulation of quantized vortices in a Bose-Einstein condensate
We experimentally and numerically demonstrate deterministic creation and
manipulation of a pair of oppositely charged singly quantized vortices in a
highly oblate Bose-Einstein condensate (BEC). Two identical blue-detuned,
focused Gaussian laser beams that pierce the BEC serve as repulsive obstacles
for the superfluid atomic gas; by controlling the positions of the beams within
the plane of the BEC, superfluid flow is deterministically established around
each beam such that two vortices of opposite circulation are generated by the
motion of the beams, with each vortex pinned to the \emph{in situ} position of
a laser beam. We study the vortex creation process, and show that the vortices
can be moved about within the BEC by translating the positions of the laser
beams. This technique can serve as a building block in future experimental
techniques to create, on-demand, deterministic arrangements of few or many
vortices within a BEC for precise studies of vortex dynamics and vortex
interactions.Comment: 9 pages, 7 figure
STOL Simulation Requirements for Development of Integrated Flight/propulsion Control Systems
The role and use of simulation as a design tool in developing integrated systems where design criteria is largely unavailable is well known. This paper addresses additional simulation needs for the development of Integrated Flight/Propulsion Control Systems (IFPCS) which will improve the probability of properly interpreting simulation results. These needs are based on recent experience with power approach flying qualities evaluations of an advanced fighter configuration which incorporated Short Takeoff and Landing (STOL) technologies and earlier experiences with power approach flying qualities evaluations on the AFTI/F-16 program. The use of motion base platforms with axial and normal degrees of freedom will help in evaluating pilot coupling and workload in the presence of high frequency low amplitude axial accelerations produced by high bandwidth airspeed controllers in a gusty environment
Emergent Semiclassical Time in Quantum Gravity. Full Geometrodynamics and Minisuperspace Examples
I apply the preceding paper's semiclassical treatment to geometrodynamics.
The analogy between the two papers is quite useful at the level of the
quadratic constraints, while I document the differences between the two due to
the underlying differences in their linear constraints. I provide a specific
minisuperspace example for my emergent semiclassical time scheme and compare it
with the hidden York time scheme. Overall, interesting connections are shown
between Newtonian, Leibniz--Mach--Barbour, WKB and cosmic times, while the
Euler and York hidden dilational times are argued to be somewhat different from
these.Comment: References Update
The Link between General Relativity and Shape Dynamics
We show that one can construct two equivalent gauge theories from a linking
theory and give a general construction principle for linking theories which we
use to construct a linking theory that proves the equivalence of General
Relativity and Shape Dynamics, a theory with fixed foliation but spatial
conformal invariance. This streamlines the rather complicated construction of
this equivalence performed previously. We use this streamlined argument to
extend the result to General Relativity with asymptotically flat boundary
conditions. The improved understanding of linking theories naturally leads to
the Lagrangian formulation of Shape Dynamics, which allows us to partially
relate the degrees of freedom.Comment: 19 pages, LaTeX, no figure
Triangleland. I. Classical dynamics with exchange of relative angular momentum
In Euclidean relational particle mechanics, only relative times, relative
angles and relative separations are meaningful. Barbour--Bertotti (1982) theory
is of this form and can be viewed as a recovery of (a portion of) Newtonian
mechanics from relational premises. This is of interest in the absolute versus
relative motion debate and also shares a number of features with the
geometrodynamical formulation of general relativity, making it suitable for
some modelling of the problem of time in quantum gravity. I also study
similarity relational particle mechanics (`dynamics of pure shape'), in which
only relative times, relative angles and {\sl ratios of} relative separations
are meaningful. This I consider firstly as it is simpler, particularly in 1 and
2 d, for which the configuration space geometry turns out to be well-known,
e.g. S^2 for the `triangleland' (3-particle) case that I consider in detail.
Secondly, the similarity model occurs as a sub-model within the Euclidean
model: that admits a shape--scale split. For harmonic oscillator like
potentials, similarity triangleland model turns out to have the same
mathematics as a family of rigid rotor problems, while the Euclidean case turns
out to have parallels with the Kepler--Coulomb problem in spherical and
parabolic coordinates. Previous work on relational mechanics covered cases
where the constituent subsystems do not exchange relative angular momentum,
which is a simplifying (but in some ways undesirable) feature paralleling
centrality in ordinary mechanics. In this paper I lift this restriction. In
each case I reduce the relational problem to a standard one, thus obtain
various exact, asymptotic and numerical solutions, and then recast these into
the original mechanical variables for physical interpretation.Comment: Journal Reference added, minor updates to References and Figure
- …