2,401 research outputs found
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
On the temperature dependence of the interaction-induced entanglement
Both direct and indirect weak nonresonant interactions are shown to produce
entanglement between two initially disentangled systems prepared as a tensor
product of thermal states, provided the initial temperature is sufficiently
low. Entanglement is determined by the Peres-Horodeckii criterion, which
establishes that a composite state is entangled if its partial transpose is not
positive. If the initial temperature of the thermal states is higher than an
upper critical value the minimal eigenvalue of the partially
transposed density matrix of the composite state remains positive in the course
of the evolution. If the initial temperature of the thermal states is lower
than a lower critical value the minimal eigenvalue of the
partially transposed density matrix of the composite state becomes negative
which means that entanglement develops. We calculate the lower bound
for and show that the negativity of the composite state is negligibly
small in the interval . Therefore the lower bound temperature
can be considered as \textit{the} critical temperature for the
generation of entanglement.Comment: 27 pages and 7 figure
Casimir forces from a loop integral formulation
We reformulate the Casimir force in the presence of a non-trivial background.
The force may be written in terms of loop variables, the loop being a curve
around the scattering sites. A natural path ordering of exponentials take place
when a particular representation of the scattering centres is given. The basic
object to be evaluated is a reduced (or abbreviated) classical pseudo-action
that can be operator valued.Comment: references added, text clarified in place
Numerical simulations of neutron star-black hole binaries in the near-equal-mass regime
Simulations of neutron star-black hole (NSBH) binaries generally consider
black holes with masses in the range , where we expect to find
most stellar mass black holes. The existence of lower mass black holes,
however, cannot be theoretically ruled out. Low-mass black holes in binary
systems with a neutron star companion could mimic neutron star-neutron (NSNS)
binaries, as they power similar gravitational wave (GW) and electromagnetic
(EM) signals. To understand the differences and similarities between NSNS
mergers and low-mass NSBH mergers, numerical simulations are required. Here, we
perform a set of simulations of low-mass NSBH mergers, including systems
compatible with GW170817. Our simulations use a composition and temperature
dependent equation of state (DD2) and approximate neutrino transport, but no
magnetic fields. We find that low-mass NSBH mergers produce remnant disks
significantly less massive than previously expected, and consistent with the
post-merger outflow mass inferred from GW170817 for moderately asymmetric mass
ratio. The dynamical ejecta produced by systems compatible with GW170817 is
negligible except if the mass ratio and black hole spin are at the edge of the
allowed parameter space. That dynamical ejecta is cold, neutron-rich, and
surprisingly slow for ejecta produced during the tidal disruption of a neutron
star : . We also find that the final mass of the remnant
black hole is consistent with existing analytical predictions, while the final
spin of that black hole is noticeably larger than expected -- up to for our equal mass case
Explicit solution of the linearized Einstein equations in TT gauge for all multipoles
We write out the explicit form of the metric for a linearized gravitational
wave in the transverse-traceless gauge for any multipole, thus generalizing the
well-known quadrupole solution of Teukolsky. The solution is derived using the
generalized Regge-Wheeler-Zerilli formalism developed by Sarbach and Tiglio.Comment: 9 pages. Minor corrections, updated references. Final version to
appear in Class. Quantum Gra
Treating instabilities in a hyperbolic formulation of Einstein's equations
We have recently constructed a numerical code that evolves a spherically
symmetric spacetime using a hyperbolic formulation of Einstein's equations. For
the case of a Schwarzschild black hole, this code works well at early times,
but quickly becomes inaccurate on a time scale of 10-100 M, where M is the mass
of the hole. We present an analytic method that facilitates the detection of
instabilities. Using this method, we identify a term in the evolution equations
that leads to a rapidly-growing mode in the solution. After eliminating this
term from the evolution equations by means of algebraic constraints, we can
achieve free evolution for times exceeding 10000M. We discuss the implications
for three-dimensional simulations.Comment: 13 pages, 9 figures. To appear in Phys. Rev.
Energy Norms and the Stability of the Einstein Evolution Equations
The Einstein evolution equations may be written in a variety of equivalent
analytical forms, but numerical solutions of these different formulations
display a wide range of growth rates for constraint violations. For symmetric
hyperbolic formulations of the equations, an exact expression for the growth
rate is derived using an energy norm. This expression agrees with the growth
rate determined by numerical solution of the equations. An approximate method
for estimating the growth rate is also derived. This estimate can be evaluated
algebraically from the initial data, and is shown to exhibit qualitatively the
same dependence as the numerically-determined rate on the parameters that
specify the formulation of the equations. This simple rate estimate therefore
provides a useful tool for finding the most well-behaved forms of the evolution
equations.Comment: Corrected typos; to appear in Physical Review
Van-der-Waals potentials of paramagnetic atoms
We study single- and two-atom van der Waals interactions of ground-state
atoms which are both polarizable and paramagnetizable in the presence of
magneto-electric bodies within the framework of macroscopic quantum
electrodynamics. Starting from an interaction Hamiltonian that includes
particle spins, we use leading-order perturbation theory for the van der Waals
potentials expressed in terms of the polarizability and magnetizability of the
atom(s). To allow for atoms embedded in media, we also include local-field
corrections via the real-cavity model. The general theory is applied to the
potential of a single atom near a half space and that of two atoms embedded in
a bulk medium or placed near a sphere, respectively.Comment: 18 pages, 3 figures, 1 tabl
Numerical Evolution of Black Holes with a Hyperbolic Formulation of General Relativity
We describe a numerical code that solves Einstein's equations for a
Schwarzschild black hole in spherical symmetry, using a hyperbolic formulation
introduced by Choquet-Bruhat and York. This is the first time this formulation
has been used to evolve a numerical spacetime containing a black hole. We
excise the hole from the computational grid in order to avoid the central
singularity. We describe in detail a causal differencing method that should
allow one to stably evolve a hyperbolic system of equations in three spatial
dimensions with an arbitrary shift vector, to second-order accuracy in both
space and time. We demonstrate the success of this method in the spherically
symmetric case.Comment: 23 pages RevTeX plus 7 PostScript figures. Submitted to Phys. Rev.
Constructing hyperbolic systems in the Ashtekar formulation of general relativity
Hyperbolic formulations of the equations of motion are essential technique
for proving the well-posedness of the Cauchy problem of a system, and are also
helpful for implementing stable long time evolution in numerical applications.
We, here, present three kinds of hyperbolic systems in the Ashtekar formulation
of general relativity for Lorentzian vacuum spacetime. We exhibit several (I)
weakly hyperbolic, (II) diagonalizable hyperbolic, and (III) symmetric
hyperbolic systems, with each their eigenvalues. We demonstrate that Ashtekar's
original equations form a weakly hyperbolic system. We discuss how gauge
conditions and reality conditions are constrained during each step toward
constructing a symmetric hyperbolic system.Comment: 15 pages, RevTeX, minor changes in Introduction. published as Int. J.
Mod. Phys. D 9 (2000) 1
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