2,698 research outputs found
Simulating merging binary black holes with nearly extremal spins
Astrophysically realistic black holes may have spins that are nearly extremal
(i.e., close to 1 in dimensionless units). Numerical simulations of binary
black holes are important tools both for calibrating analytical templates for
gravitational-wave detection and for exploring the nonlinear dynamics of curved
spacetime. However, all previous simulations of binary-black-hole inspiral,
merger, and ringdown have been limited by an apparently insurmountable barrier:
the merging holes' spins could not exceed 0.93, which is still a long way from
the maximum possible value in terms of the physical effects of the spin. In
this paper, we surpass this limit for the first time, opening the way to
explore numerically the behavior of merging, nearly extremal black holes.
Specifically, using an improved initial-data method suitable for binary black
holes with nearly extremal spins, we simulate the inspiral (through 12.5
orbits), merger and ringdown of two equal-mass black holes with equal spins of
magnitude 0.95 antialigned with the orbital angular momentum.Comment: 4 pages, 2 figures, updated with version accepted for publication in
Phys. Rev. D, removed a plot that was incorrectly included at the end of the
article in version v
Characterization of the domain chaos convection state by the largest Lyapunov exponent
Using numerical integrations of the Boussinesq equations in rotating cylindrical domains with realistic boundary conditions, we have computed the value of the largest Lyapunov exponent lambda1 for a variety of aspect ratios and driving strengths. We study in particular the domain chaos state, which bifurcates supercritically from the conducting fluid state and involves extended propagating fronts as well as point defects. We compare our results with those from Egolf et al., [Nature 404, 733 (2000)], who suggested that the value of lambda1 for the spiral defect chaos state of a convecting fluid was determined primarily by bursts of instability arising from short-lived, spatially localized dislocation nucleation events. We also show that the quantity lambda1 is not intensive for aspect ratios Gamma over the range 20<Gamma<40 and that the scaling exponent of lambda1 near onset is consistent with the value predicted by the amplitude equation formalism
The effect of symmetry breaking on the dynamics near a structurally stable heteroclinic cycle between equilibria and a periodic orbit
The effect of small forced symmetry breaking on the dynamics near a structurally stable heteroclinic
cycle connecting two equilibria and a periodic orbit is investigated. This type of system is known
to exhibit complicated, possibly chaotic dynamics including irregular switching of sign of various
phase space variables, but details of the mechanisms underlying the complicated dynamics have
not previously been investigated. We identify global bifurcations that induce the onset of chaotic
dynamics and switching near a heteroclinic cycle of this type, and by construction and analysis
of approximate return maps, locate the global bifurcations in parameter space. We find there is a
threshold in the size of certain symmetry-breaking terms below which there can be no persistent
switching. Our results are illustrated by a numerical example
On the equivalence of the Langevin and auxiliary field quantization methods for absorbing dielectrics
Recently two methods have been developed for the quantization of the
electromagnetic field in general dispersing and absorbing linear dielectrics.
The first is based upon the introduction of a quantum Langevin current in
Maxwell's equations [T. Gruner and D.-G. Welsch, Phys. Rev. A 53, 1818 (1996);
Ho Trung Dung, L. Kn\"{o}ll, and D.-G. Welsch, Phys. Rev. A 57, 3931 (1998); S.
Scheel, L. Kn\"{o}ll, and D.-G. Welsch, Phys. Rev. A 58, 700 (1998)], whereas
the second makes use of a set of auxiliary fields, followed by a canonical
quantization procedure [A. Tip, Phys. Rev. A 57, 4818 (1998)]. We show that
both approaches are equivalent.Comment: 7 pages, RevTeX, no figure
Coincident count rates in absorbing dielectric media
A study of the effects of absorption on the nonlinear process of parametric
down conversion is presented. Absorption within the nonlinear medium is
accounted for by employing the framework of macroscopic QED and the Green
tensor quantization of the electromagnetic field. An effective interaction
Hamiltonian, which describes the nonlinear interaction of the electric field
and the linear noise polarization field, is used to derive the quantum state of
the light leaving a nonlinear crystal. The signal and idler modes of this
quantum state are found to be a superpositions of the electric and noise
polarization fields. Using this state, the expression for the coincident count
rates for both Type I and Type II conversion are found. The nonlinear
interaction with the noise polarization field were shown to cause an increase
in the rate on the order of 10^{-12} for absorption of 10% per cm. This
astonishingly small effect is found to be negligible compared to the decay
caused by linear absorption of the propagating modes. From the expressions for
the biphoton amplitude it can be seen the maximally entangled states can still
be produced even in the presence of strong absorption.Comment: Updated to journal version. 10 Pages, 8 figure
Upper bounds on success probabilities in linear optics
We develop an abstract way of defining linear-optics networks designed to
perform quantum information tasks such as quantum gates. We will be mainly
concerned with the nonlinear sign shift gate, but it will become obvious that
all other gates can be treated in a similar manner. The abstract scheme is
extremely well suited for analytical as well as numerical investigations since
it reduces the number of parameters for a general setting. With that we show
numerically and partially analytically for a wide class of states that the
success probability of generating a nonlinear sign shift gate does not exceed
1/4 which to our knowledge is the strongest bound to date.Comment: 8 pages, typeset using RevTex4, 5 EPS figure
Casimir-Polder interaction between an atom and a small magnetodielectric sphere
On the basis of macroscopic quantum electrodynamics and point-scattering
techniques, we derive a closed expression for the Casimir-Polder force between
a ground-state atom and a small magnetodielectric sphere in an arbitrary
environment. In order to allow for the presence of both bodies and media,
local-field corrections are taken into account. Our results are compared with
the known van der Waals force between two ground-state atoms. To continuously
interpolate between the two extreme cases of a single atom and a macroscopic
sphere, we also derive the force between an atom and a sphere of variable
radius that is embedded in an Onsager local-field cavity. Numerical examples
illustrate the theory.Comment: 9 pages, 4 figures, minor addition
Energy as an Entanglement Witness for Quantum Many-Body Systems
We investigate quantum many-body systems where all low-energy states are
entangled. As a tool for quantifying such systems, we introduce the concept of
the entanglement gap, which is the difference in energy between the
ground-state energy and the minimum energy that a separable (unentangled) state
may attain. If the energy of the system lies within the entanglement gap, the
state of the system is guaranteed to be entangled. We find Hamiltonians that
have the largest possible entanglement gap; for a system consisting of two
interacting spin-1/2 subsystems, the Heisenberg antiferromagnet is one such
example. We also introduce a related concept, the entanglement-gap temperature:
the temperature below which the thermal state is certainly entangled, as
witnessed by its energy. We give an example of a bipartite Hamiltonian with an
arbitrarily high entanglement-gap temperature for fixed total energy range. For
bipartite spin lattices we prove a theorem demonstrating that the entanglement
gap necessarily decreases as the coordination number is increased. We
investigate frustrated lattices and quantum phase transitions as physical
phenomena that affect the entanglement gap.Comment: 16 pages, 3 figures, published versio
Black Hole--Scalar Field Interactions in Spherical Symmetry
We examine the interactions of a black hole with a massless scalar field
using a coordinate system which extends ingoing Eddington-Finkelstein
coordinates to dynamic spherically symmetric-spacetimes. We avoid problems with
the singularity by excising the region of the black hole interior to the
apparent horizon. We use a second-order finite difference scheme to solve the
equations. The resulting program is stable and convergent and will run forever
without problems. We are able to observe quasi-normal ringing and power-law
tails as well an interesting nonlinear feature.Comment: 16 pages, 26 figures, RevTex, to appear in Phys. Rev.
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