50 research outputs found
Closed Strings with Low Harmonics and Kinks
Low-harmonic formulas for closed relativistic strings are given. General
parametrizations are presented for the addition of second- and third-harmonic
waves to the fundamental wave. The method of determination of the
parametrizations is based upon a product representation found for the finite
Fourier series of string motion in which the constraints are automatically
satisfied. The construction of strings with kinks is discussed, including
examples. A procedure is laid out for the representation of kinks that arise
from self-intersection, and subsequent intercommutation, for harmonically
parametrized cosmic strings.Comment: 39, CWRUTH-93-
Bohmian arrival time without trajectories
The computation of detection probabilities and arrival time distributions
within Bohmian mechanics in general needs the explicit knowledge of a relevant
sample of trajectories. Here it is shown how for one-dimensional systems and
rigid inertial detectors these quantities can be computed without calculating
any trajectories. An expression in terms of the wave function and its spatial
derivative, both restricted to the boundary of the detector's spacetime volume,
is derived for the general case, where the probability current at the
detector's boundary may vary its sign.Comment: 20 pages, 12 figures; v2: reference added, extended introduction,
published versio
Evolution of cosmic string configurations
We extend and develop our previous work on the evolution of a network of
cosmic strings. The new treatment is based on an analysis of the probability
distribution of the end-to-end distance of a randomly chosen segment of
left-moving string of given length. The description involves three distinct
length scales: , related to the overall string density, , the
persistence length along the string, and , describing the small-scale
structure, which is an important feature of the numerical simulations that have
been done of this problem. An evolution equation is derived describing how the
distribution develops in time due to the combined effects of the universal
expansion, of intercommuting and loop formation, and of gravitational
radiation. With plausible assumptions about the unknown parameters in the
model, we confirm the conclusions of our previous study, that if gravitational
radiation and small-scale structure effects are neglected, the two dominant
length scales both scale in proportion to the horizon size. When the extra
effects are included, we find that while and grow,
initially does not. Eventually, however, it does appear to scale, at a much
lower level, due to the effects of gravitational back-reaction.Comment: 61 pages, requires RevTex v3.0, SUSSEX-TH-93/3-4,
IMPERIAL/TP/92-93/4
Signature Change on the Brane
We explore the possibility of having a good description of classical
signature change in the brane scenario.Comment: RevTeX, 4 pages, 1 figure. Uses epsfig package. Slightly shorter
version to match the published version. Reference adde
General solutions of Einstein's spherically symmetric gravitational equations with junction conditions
Einstein's spherically symmetric interior gravitational equations are
investigated. Following Synge's procedure, the most general solution of the
equations is furnished in case and are prescribed. The
existence of a total mass function, , is rigorously proved. Under
suitable restrictions on the total mass function, the Schwarzschild mass
, implicitly defines the boundary of the spherical body as .
Both Synge's junction conditions as well as the continuity of the second
fundamental form are examined and solved in a general manner. The weak energy
conditions for an \emph{arbitrary boost} are also considered. The most general
solution of the spherically symmetric anisotropic fluid model satisfying both
junction conditions is furnished. In the final section, various exotic
solutions are explored using the developed scheme including gravitational
instantons, interior -domains and -dimensional generalizations.Comment: 23 pages, 1 figure, uses AMS packages. Updated version has corrected
typos as well as added comments and extension regarding ISLD junction
conditions. Accepted for publication in Journal of Mathematical Physic
Spacetime Coarse Grainings in the Decoherent Histories Approach to Quantum Theory
We investigate the possibility of assigning consistent probabilities to sets
of histories characterized by whether they enter a particular subspace of the
Hilbert space of a closed system during a given time interval. In particular we
investigate the case that this subspace is a region of the configuration space.
This corresponds to a particular class of coarse grainings of spacetime
regions. We consider the arrival time problem and the problem of time in
reparametrization invariant theories as for example in canonical quantum
gravity. Decoherence conditions and probabilities for those application are
derived. The resulting decoherence condition does not depend on the explicit
form of the restricted propagator that was problematic for generalizations such
as application in quantum cosmology. Closely related is the problem of
tunnelling time as well as the quantum Zeno effect. Some interpretational
comments conclude, and we discuss the applicability of this formalism to deal
with the arrival time problem.Comment: 23 pages, Few changes and added references in v
Decoherent histories analysis of the relativistic particle
The Klein-Gordon equation is a useful test arena for quantum cosmological
models described by the Wheeler-DeWitt equation. We use the decoherent
histories approach to quantum theory to obtain the probability that a free
relativistic particle crosses a section of spacelike surface. The decoherence
functional is constructed using path integral methods with initial states
attached using the (positive definite) ``induced'' inner product between
solutions to the constraint equation. The notion of crossing a spacelike
surface requires some attention, given that the paths in the path integral may
cross such a surface many times, but we show that first and last crossings are
in essence the only useful possibilities. Different possible results for the
probabilities are obtained, depending on how the relativistic particle is
quantized (using the Klein-Gordon equation, or its square root, with the
associated Newton-Wigner states). In the Klein-Gordon quantization, the
decoherence is only approximate, due to the fact that the paths in the path
integral may go backwards and forwards in time. We compare with the results
obtained using operators which commute with the constraint (the ``evolving
constants'' method).Comment: 51 pages, plain Te
Probabilities in Quantum Cosmological Models: A Decoherent Histories Analysis Using a Complex Potential
In the quantization of simple cosmological models (minisuperspace models)
described by the Wheeler-DeWitt equation, an important step is the
construction, from the wave function, of a probability distribution answering
various questions of physical interest, such as the probability of the system
entering a given region of configuration space at any stage in its entire
history. A standard but heuristic procedure is to use the flux of (components
of) the wave function in a WKB approximation. This gives sensible semiclassical
results but lacks an underlying operator formalism. In this paper, we address
the issue of constructing probability distributions linked to the
Wheeler-DeWitt equation using the decoherent histories approach to quantum
theory. We show that the appropriate class operators (the generalization of
strings of projectors) in quantum cosmology are readily constructed using a
complex potential. We derive the class operator for entering or not entering
one or more regions in configuration space. They commute with the Hamiltonian,
have a sensible classical limit and are closely related to intersection number
operators. We show that oscillatory WKB solutions to the Wheeler-DeWitt
equation give approximate decoherence of histories, as do superpositions of WKB
solutions, as long as the regions of configuration space are sufficiently
large. The corresponding probabilities coincide, in a semiclassical
approximation, with standard heuristic procedures. In brief, we exhibit the
well-defined operator formalism underlying the usual heuristic interpretational
methods in quantum cosmology.Comment: 49 pages, Latex, 8 figure
Demographic and clinical correlates of autism symptom domains and autism spectrum diagnosis
Demographic and clinical factors may influence assessment of autism symptoms. This study evaluated these correlates and also examined whether social communication and interaction and restricted/repetitive behavior provided unique prediction of autism spectrum disorder diagnosis. We analyzed data from 7352 siblings included in the Interactive Autism Network registry. Social communication and interaction and restricted/repetitive behavior symptoms were obtained using caregiver-reports on the Social Responsiveness Scale. Demographic and clinical correlates were covariates in regression models predicting social communication and interaction and restricted/repetitive behavior symptoms. Logistic regression and receiver operating characteristic curve analyses evaluated the incremental validity of social communication and interaction and restricted/repetitive behavior domains over and above global autism symptoms. Autism spectrum disorder diagnosis was the strongest correlate of caregiver-reported social communication and interaction and restricted/repetitive behavior symptoms. The presence of comorbid diagnoses also increased symptom levels. Social communication and interaction and restricted/repetitive behavior symptoms provided significant, but modest, incremental validity in predicting diagnosis beyond global autism symptoms. These findings suggest that autism spectrum disorder diagnosis is by far the largest determinant of quantitatively measured autism symptoms. Externalizing (attention deficit hyperactivity disorder) and internalizing (anxiety) behavior, low cognitive ability, and demographic factors may confound caregiver-report of autism symptoms, potentially necessitating a continuous norming approach to the revision of symptom measures. Social communication and interaction and restricted/repetitive behavior symptoms may provide incremental validity in the diagnosis of autism spectrum disorder
Trajectories for the Wave Function of the Universe from a Simple Detector Model
Inspired by Mott's (1929) analysis of particle tracks in a cloud chamber, we
consider a simple model for quantum cosmology which includes, in the total
Hamiltonian, model detectors registering whether or not the system, at any
stage in its entire history, passes through a series of regions in
configuration space. We thus derive a variety of well-defined formulas for the
probabilities for trajectories associated with the solutions to the
Wheeler-DeWitt equation. The probability distribution is peaked about classical
trajectories in configuration space. The ``measured'' wave functions still
satisfy the Wheeler-DeWitt equation, except for small corrections due to the
disturbance of the measuring device. With modified boundary conditions, the
measurement amplitudes essentially agree with an earlier result of Hartle
derived on rather different grounds. In the special case where the system is a
collection of harmonic oscillators, the interpretation of the results is aided
by the introduction of ``timeless'' coherent states -- eigenstates of the
Hamiltonian which are concentrated about entire classical trajectories.Comment: 37 pages, plain Tex. Second draft. Substantial revision