3,184 research outputs found
Reflection and Transmission at the Apparent Horizon during Gravitational Collapse
We examine the wave-functionals describing the collapse of a self-gravitating
dust ball in an exact quantization of the gravity-dust system. We show that
ingoing (collapsing) dust shell modes outside the apparent horizon must
necessarily be accompanied by outgoing modes inside the apparent horizon, whose
amplitude is suppressed by the square root of the Boltzmann factor at the
Hawking temperature. Likewise, ingoing modes in the interior must be
accompanied by outgoing modes in the exterior, again with an amplitude
suppressed by the same factor. A suitable superposition of the two solutions is
necessary to conserve the dust probability flux across the apparent horizon,
thus each region contains both ingoing and outgoing dust modes. If one
restricts oneself to considering only the modes outside the apparent horizon
then one should think of the apparent horizon as a partial reflector, the
probability for a shell to reflect being given by the Boltzmann factor at the
Hawking temperature determined by the mass contained within it. However, if one
considers the entire wave function, the outgoing wave in the exterior is seen
to be the transmission through the horizon of the interior outgoing wave that
accompanies the collapsing shells. This transmission could allow information
from the interior to be transferred to the exterior.Comment: 19 pages, no figures. To appear in Phys. Rev.
On the relation between adjacent inviscid cell type solutions to the rotating-disk equations
Over a large range of the axial coordinate a typical higher-branch solution of the rotating-disk equations consists of a chain of inviscid cells separated from each other by viscous interlayers. In this paper the leading-order relation between two adjacent cells will be established by matched asymptotic expansions for general values of the parameter appearing in the equations. It is found that the relation between the solutions in the two cells crucially depends on the behaviour of the tangential velocity in the viscous interlayer. The results of the theory are compared with accurate numerical solutions and good agreement is obtained
Coagulation kinetics beyond mean field theory using an optimised Poisson representation
Binary particle coagulation can be modelled as the repeated random process of
the combination of two particles to form a third. The kinetics can be
represented by population rate equations based on a mean field assumption,
according to which the rate of aggregation is taken to be proportional to the
product of the mean populations of the two participants. This can be a poor
approximation when the mean populations are small. However, using the Poisson
representation it is possible to derive a set of rate equations that go beyond
mean field theory, describing pseudo-populations that are continuous, noisy and
complex, but where averaging over the noise and initial conditions gives the
mean of the physical population. Such an approach is explored for the simple
case of a size-independent rate of coagulation between particles. Analytical
results are compared with numerical computations and with results derived by
other means. In the numerical work we encounter instabilities that can be
eliminated using a suitable 'gauge' transformation of the problem [P. D.
Drummond, Eur. Phys. J. B38, 617 (2004)] which we show to be equivalent to the
application of the Cameron-Martin-Girsanov formula describing a shift in a
probability measure. The cost of such a procedure is to introduce additional
statistical noise into the numerical results, but we identify an optimised
gauge transformation where this difficulty is minimal for the main properties
of interest. For more complicated systems, such an approach is likely to be
computationally cheaper than Monte Carlo simulation
The Renormalized Stress Tensor in Kerr Space-Time: Numerical Results for the Hartle-Hawking Vacuum
We show that the pathology which afflicts the Hartle-Hawking vacuum on the
Kerr black hole space-time can be regarded as due to rigid rotation of the
state with the horizon in the sense that when the region outside the
speed-of-light surface is removed by introducing a mirror, there is a state
with the defining features of the Hartle-Hawking vacuum. In addition, we show
that when the field is in this state, the expectation value of the
energy-momentum stress tensor measured by an observer close to the horizon and
rigidly rotating with it corresponds to that of a thermal distribution at the
Hawking temperature rigidly rotating with the horizon.Comment: 17 pages, 7 figure
Stability of Topological Black Holes
We explore the classical stability of topological black holes in
d-dimensional anti-de Sitter spacetime, where the horizon is an Einstein
manifold of negative curvature. According to the gauge invariant formalism of
Ishibashi and Kodama, gravitational perturbations are classified as being of
scalar, vector, or tensor type, depending on their transformation properties
with respect to the horizon manifold. For the massless black hole, we show that
the perturbation equations for all modes can be reduced to a simple scalar
field equation. This equation is exactly solvable in terms of hypergeometric
functions, thus allowing an exact analytic determination of potential
gravitational instabilities. We establish a necessary and sufficient condition
for stability, in terms of the eigenvalues of the Lichnerowicz
operator on the horizon manifold, namely . For the case
of negative mass black holes, we show that a sufficient condition for stability
is given by .Comment: 20 pages, Latex, v2 refined analysis of boundary conditions in
dimensions 4,5,6, additional reference
Solvable Examples of Drift and Diffusion of Ions in Non-uniform Electric Fields
The drift and diffusion of a cloud of ions in a fluid are distorted by an
inhomogeneous electric field. If the electric field carries the center of the
distribution in a straight line and the field configuration is suitably
symmetric, the distortion can be calculated analytically. We examine the
specific examples of fields with cylindrical and spherical symmetry in detail
assuming the ion distributions to be of a generally Gaussian form. The effects
of differing diffusion coefficients in the transverse and longitudinal
directions are included
Cooperative scattering and radiation pressure force in dense atomic clouds
We consider the collective scattering by a cloud of two-level atoms
driven by an uniform radiation field. Dense atomic clouds can be described by a
continuous density and the problem reduces to deriving the spectrum of the
atom-atom coupling operator. For clouds much larger than the optical
wavelength, the spectrum is treated as a continuum, and analytical expressions
for several macroscopic quantities, such as scattered radiation intensity and
radiation pressure force, are derived. The analytical results are then compared
to the exact -body solution and with those obtained assuming a symmetric
timed Dicke state. In contrast with the symmetric timed Dicke state, our
calculations takes account of the back action of the atoms on the driving field
leading to phase shifts due to the finite refraction of the cloud
Vector and Tensor Contributions to the Luminosity Distance
We compute the vector and tensor contributions to the luminosity distance
fluctuations in first order perturbation theory and we expand them in spherical
harmonics. This work presents the formalism with a first application to a
stochastic background of primordial gravitational waves.Comment: 14 pages, 3 figure
Fingerprinting Soft Materials: A Framework for Characterizing Nonlinear Viscoelasticity
We introduce a comprehensive scheme to physically quantify both viscous and
elastic rheological nonlinearities simultaneously, using an imposed large
amplitude oscillatory shear (LAOS) strain. The new framework naturally lends a
physical interpretation to commonly reported Fourier coefficients of the
nonlinear stress response. Additionally, we address the ambiguities inherent in
the standard definitions of viscoelastic moduli when extended into the
nonlinear regime, and define new measures which reveal behavior that is
obscured by conventional techniques.Comment: 10 pages, 3 figures, full-page double-space preprint forma
Preparation information and optimal decompositions for mixed quantum states
Consider a joint quantum state of a system and its environment. A measurement
on the environment induces a decomposition of the system state. Using
algorithmic information theory, we define the preparation information of a pure
or mixed state in a given decomposition. We then define an optimal
decomposition as a decomposition for which the average preparation information
is minimal. The average preparation information for an optimal decomposition
characterizes the system-environment correlations. We discuss properties and
applications of the concepts introduced above and give several examples.Comment: 13 pages, latex, 2 postscript figure
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