1,640 research outputs found
Chaos in Quantum Cosmology
Much of the foundational work on quantum cosmology employs a simple
minisuperspace model describing a Friedmann-Robertson-Walker universe
containing a massive scalar field. We show that the classical limit of this
model exhibits deterministic chaos and explore some of the consequences for the
quantum theory. In particular, the breakdown of the WKB approximation calls
into question many of the standard results in quantum cosmology.Comment: 4 pages, 4 figures, RevTex two column style. Minor revisions and
clarifications to reflect version published in Phys. Rev. Let
Chaotic Scattering and Capture of Strings by Black Hole
We consider scattering and capture of circular cosmic strings by a
Schwarzschild black hole. Although being a priori a very simple axially
symmetric two-body problem, it shows all the features of chaotic scattering. In
particular, it contains a fractal set of unstable periodic solutions; a
so-called strange repellor. We study the different types of trajectories and
obtain the fractal dimension of the basin-boundary separating the space of
initial conditions according to the different asymptotic outcomes. We also
consider the fractal dimension as a function of energy, and discuss the
transition from order to chaos.Comment: RevTeX 3.1, 9 pages, 5 figure
How accurate are the non-linear chemical Fokker-Planck and chemical Langevin equations?
The chemical Fokker-Planck equation and the corresponding chemical Langevin
equation are commonly used approximations of the chemical master equation.
These equations are derived from an uncontrolled, second-order truncation of
the Kramers-Moyal expansion of the chemical master equation and hence their
accuracy remains to be clarified. We use the system-size expansion to show that
chemical Fokker-Planck estimates of the mean concentrations and of the variance
of the concentration fluctuations about the mean are accurate to order
for reaction systems which do not obey detailed balance and at
least accurate to order for systems obeying detailed balance,
where is the characteristic size of the system. Hence the chemical
Fokker-Planck equation turns out to be more accurate than the linear-noise
approximation of the chemical master equation (the linear Fokker-Planck
equation) which leads to mean concentration estimates accurate to order
and variance estimates accurate to order . This
higher accuracy is particularly conspicuous for chemical systems realized in
small volumes such as biochemical reactions inside cells. A formula is also
obtained for the approximate size of the relative errors in the concentration
and variance predictions of the chemical Fokker-Planck equation, where the
relative error is defined as the difference between the predictions of the
chemical Fokker-Planck equation and the master equation divided by the
prediction of the master equation. For dimerization and enzyme-catalyzed
reactions, the errors are typically less than few percent even when the
steady-state is characterized by merely few tens of molecules.Comment: 39 pages, 3 figures, accepted for publication in J. Chem. Phy
Homoclinic chaos in the dynamics of a general Bianchi IX model
The dynamics of a general Bianchi IX model with three scale factors is
examined. The matter content of the model is assumed to be comoving dust plus a
positive cosmological constant. The model presents a critical point of
saddle-center-center type in the finite region of phase space. This critical
point engenders in the phase space dynamics the topology of stable and unstable
four dimensional tubes , where is a saddle direction and
is the manifold of unstable periodic orbits in the center-center sector.
A general characteristic of the dynamical flow is an oscillatory mode about
orbits of an invariant plane of the dynamics which contains the critical point
and a Friedmann-Robertson-Walker (FRW) singularity. We show that a pair of
tubes (one stable, one unstable) emerging from the neighborhood of the critical
point towards the FRW singularity have homoclinic transversal crossings. The
homoclinic intersection manifold has topology and is constituted
of homoclinic orbits which are bi-asymptotic to the center-center
manifold. This is an invariant signature of chaos in the model, and produces
chaotic sets in phase space. The model also presents an asymptotic DeSitter
attractor at infinity and initial conditions sets are shown to have fractal
basin boundaries connected to the escape into the DeSitter configuration
(escape into inflation), characterizing the critical point as a chaotic
scatterer.Comment: 11 pages, 6 ps figures. Accepted for publication in Phys. Rev.
Explosion of a collapsing Bose-Einstein condensate
We show that elastic collisions between atoms in a Bose-Einstein condensate
with attractive interactions lead to an explosion that ejects a large fraction
of the collapsing condensate. We study variationally the dynamics of this
explosion and find excellent agreement with recent experiments on magnetically
trapped Rubidium-85. We also determine the energy and angular distribution of
the ejected atoms during the collapse.Comment: Four pages of ReVTeX and five postscript figure
Chaos in the Einstein-Yang-Mills Equations
Yang-Mills color fields evolve chaotically in an anisotropically expanding
universe. The chaotic behaviour differs from that found in anisotropic
Mixmaster universes. The universe isotropizes at late times, approaching the
mean expansion rate of a radiation-dominated universe. However, small chaotic
oscillations of the shear and color stresses continue indefinitely. An
invariant, coordinate-independent characterisation of the chaos is provided by
means of fractal basin boundaries.Comment: 3 pages LaTeX + 3 pages of figure
Stability analysis and quasinormal modes of Reissner Nordstr{\o}m Space-time via Lyapunov exponent
We explicitly derive the proper time principal Lyapunov exponent
() and coordinate time () principal Lyapunov exponent
() for Reissner Nordstr{\o}m (RN) black hole (BH) . We also
compute their ratio. For RN space-time, it is shown that the ratio is
for
time-like circular geodesics and for Schwarzschild BH it is
. We
further show that their ratio may vary from
orbit to orbit. For instance, Schwarzschild BH at innermost stable circular
orbit(ISCO), the ratio is
and at marginally
bound circular orbit (MBCO) the ratio is calculated to be
. Similarly, for extremal RN
BH the ratio at ISCO is
.
We also further analyse the geodesic stability via this exponent. By evaluating
the Lyapunov exponent, it is shown that in the eikonal limit , the real and
imaginary parts of the quasi-normal modes of RN BH is given by the frequency
and instability time scale of the unstable null circular geodesics.Comment: Accepted in Pramana, 07/09/201
New Algorithm for Mixmaster Dynamics
We present a new numerical algorithm for evolving the Mixmaster spacetimes.
By using symplectic integration techniques to take advantage of the exact Taub
solution for the scattering between asymptotic Kasner regimes, we evolve these
spacetimes with higher accuracy using much larger time steps than previously
possible. The longer Mixmaster evolution thus allowed enables detailed
comparison with the Belinskii, Khalatnikov, Lifshitz (BKL) approximate
Mixmaster dynamics. In particular, we show that errors between the BKL
prediction and the measured parameters early in the simulation can be
eliminated by relaxing the BKL assumptions to yield an improved map. The
improved map has different predictions for vacuum Bianchi Type IX and magnetic
Bianchi Type VI Mixmaster models which are clearly matched in the
simulation.Comment: 12 pages, Revtex, 4 eps figure
The tale of two centres
We study motion in the field of two fixed centres described by a family of
Einstein-dilaton-Maxwell theories. Transitions between regular and chaotic
motion are observed as the dilaton coupling is varied.Comment: 20 pages, RevTeX, 7 figures included, TeX format change
Studying stellar binary systems with the Laser Interferometer Space Antenna using Delayed Rejection Markov chain Monte Carlo methods
Bayesian analysis of LISA data sets based on Markov chain Monte Carlo methods
has been shown to be a challenging problem, in part due to the complicated
structure of the likelihood function consisting of several isolated local
maxima that dramatically reduces the efficiency of the sampling techniques.
Here we introduce a new fully Markovian algorithm, a Delayed Rejection
Metropolis-Hastings Markov chain Monte Carlo method, to efficiently explore
these kind of structures and we demonstrate its performance on selected LISA
data sets containing a known number of stellar-mass binary signals embedded in
Gaussian stationary noise.Comment: 12 pages, 4 figures, accepted in CQG (GWDAW-13 proceedings
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