381 research outputs found
Nonequilibrium Precursor Model for the Onset of Percolation in a Two-Phase System
Using a Boltzmann equation, we investigate the nonequilibrium dynamics of
nonperturbative fluctuations within the context of Ginzburg-Landau models. As
an illustration, we examine how a two-phase system initially prepared in a
homogeneous, low-temperature phase becomes populated by precursors of the
opposite phase as the temperature is increased. We compute the critical value
of the order parameter for the onset of percolation, which signals the
breakdown of the conventional dilute gas approximation.Comment: 4 pages, 4 eps figures (uses epsf), Revtex. Replaced with version in
press Physical Review
The initial value problem for linearized gravitational perturbations of the Schwarzschild naked singularity
The coupled equations for the scalar modes of the linearized Einstein
equations around Schwarzschild's spacetime were reduced by Zerilli to a 1+1
wave equation with a potential , on a field . For smooth metric
perturbations is singular at , the
mode harmonic number, and has a second order pole at . This is
irrelevant to the black hole exterior stability problem, where , and
, but it introduces a non trivial problem in the naked singular case
where , and the singularity appears in the relevant range of
. We solve this problem by developing a new approach to the evolution of the
even mode, based on a {\em new gauge invariant function}, -related
to by an intertwiner operator- that is a regular function of the
metric perturbation {\em for any value of }. This allows to address the
issue of evolution of gravitational perturbations in this non globally
hyperbolic background, and to complete the proof of the linear instability of
the Schwarzschild naked singularity, by showing that a previously found
unstable mode is excitable by generic initial data. This is further illustrated
by numerically solving the linearized equations for suitably chosen initial
data.Comment: typos corrected, references adde
The collision of boosted black holes: second order close limit calculations
We study the head-on collision of black holes starting from unsymmetrized,
Brill--Lindquist type data for black holes with non-vanishing initial linear
momentum. Evolution of the initial data is carried out with the ``close limit
approximation,'' in which small initial separation and momentum are assumed,
and second-order perturbation theory is used. We find agreement that is
remarkably good, and that in some ways improves with increasing momentum. This
work extends a previous study in which second order perturbation calculations
were used for momentarily stationary initial data, and another study in which
linearized perturbation theory was used for initially moving holes. In addition
to supplying answers about the collisions, the present work has revealed
several subtle points about the use of higher order perturbation theory, points
that did not arise in the previous studies. These points include issues of
normalization, and of comparison with numerical simulations, and will be
important to subsequent applications of approximation methods for collisions.Comment: 20 pages, RevTeX, 6 figures included with psfi
The collision of two slowly rotating, initially non boosted, black holes in the close limit
We study the collision of two slowly rotating, initially non boosted, black
holes in the close limit. A ``punctures'' modification of the Bowen - York
method is used to construct conformally flat initial data appropriate to the
problem. We keep only the lowest nontrivial orders capable of giving rise to
radiation of both gravitational energy and angular momentum. We show that even
with these simplifications an extension to higher orders of the linear
Regge-Wheeler-Zerilli black hole perturbation theory, is required to deal with
the evolution equations of the leading contributing multipoles. This extension
is derived, together with appropriate extensions of the Regge-Wheeler and
Zerilli equations. The data is numerically evolved using these equations, to
obtain the asymptotic gravitational wave forms and amplitudes. Expressions for
the radiated gravitational energy and angular momentum are derived and used
together with the results of the numerical evolution to provide quantitative
expressions for the relative contribution of different terms, and their
significance is analyzed.Comment: revtex, 18 pages, 2 figures. Misprints corrected. To be published in
Phys. Rev.
Resonant nucleation of spatio-temporal order via parametric modal amplification
We investigate, analytically and numerically, the emergence of
spatio-temporal order in nonequilibrium scalar field theories. The onset of
order is triggered by destabilizing interactions (DIs), which instantaneously
change the interacting potential from a single to a double-well, tunable to be
either degenerate (SDW) or nondegenerate (ADW). For the SDW case, we observe
the emergence of spatio-temporal coherent structures known as oscillons. We
show that this emergence is initially synchronized, the result of parametric
amplification of the relevant oscillon modes. We also discuss how these ordered
structures act as bottlenecks for equipartition. For ADW potentials, we show
how the same parametric amplification mechanism may trigger the rapid decay of
a metastable state. For a range of temperatures, the decay rates associated
with this resonant nucleation can be orders of magnitude larger than those
computed by homogeneous nucleation, with time-scales given by a simple power
law, , where depends weakly on the
temperature and is the free-energy barrier of a critical
fluctuation.Comment: 38 pages, 20 figures now included within the tex
Perturbative evolution of conformally flat initial data for a single boosted black hole
The conformally flat families of initial data typically used in numerical
relativity to represent boosted black holes are not those of a boosted slice of
the Schwarzschild spacetime. If such data are used for each black hole in a
collision, the emitted radiation will be partially due to the ``relaxation'' of
the individual holes to ``boosted Schwarzschild'' form. We attempt to compute
this radiation by treating the geometry for a single boosted conformally flat
hole as a perturbation of a Schwarzschild black hole, which requires the use of
second order perturbation theory. In this we attempt to mimic a previous
calculation we did for the conformally flat initial data for spinning holes. We
find that the boosted black hole case presents additional subtleties, and
although one can evolve perturbatively and compute radiated energies, it is
much less clear than in the spinning case how useful for the study of
collisions are the radiation estimates for the ``spurious energy'' in each
hole. In addition to this we draw some lessons on which frame of reference
appears as more favorable for computing black hole collisions in the close
limit approximation.Comment: 11 pages, RevTex, 4 figures included with psfig, to appear in PR
Thermal Phase Mixing During First Order Phase Transitions
The dynamics of first order phase transitions are studied in the context of
(3+1)-dimensional scalar field theories. Particular attention is paid to the
question of quantifying the strength of the transition, and how `weak' and
`strong' transitions have different dynamics. We propose a model with two
available low temperature phases separated by an energy barrier so that one of
them becomes metastable below the critical temperature . The system is
initially prepared in this phase and is coupled to a thermal bath.
Investigating the system at its critical temperature, we find that `strong'
transitions are characterized by the system remaining localized within its
initial phase, while `weak' transitions are characterized by considerable phase
mixing. Always at , we argue that the two regimes are themselves separated
by a (second order) phase transition, with an order parameter given by the
fractional population difference between the two phases and a control parameter
given by the strength of the scalar field's quartic self-coupling constant. We
obtain a Ginzburg-like criterion to distinguish between `weak' and `strong'
transitions, in agreement with previous results in (2+1)-dimensions.Comment: 28 pages RevTeX, 9 postscript figures, IMPERIAL/TP/93-94/58,
DART-HEP-94/0
Soliton Solutions with Real Poles in the Alekseev formulation of the Inverse-Scattering method
A new approach to the inverse-scattering technique of Alekseev is presented
which permits real-pole soliton solutions of the Ernst equations to be
considered. This is achieved by adopting distinct real poles in the scattering
matrix and its inverse. For the case in which the electromagnetic field
vanishes, some explicit solutions are given using a Minkowski seed metric. The
relation with the corresponding soliton solutions that can be constructed using
the Belinskii-Zakharov inverse-scattering technique is determined.Comment: 8 pages, LaTe
Drake Equation for the Multiverse: From the String Landscape to Complex Life
It is argued that selection criteria usually referred to as "anthropic
conditions" for the existence of intelligent (typical) observers widely adopted
in cosmology amount only to preconditions for primitive life. The existence of
life does not imply in the existence of intelligent life. On the contrary, the
transition from single-celled to complex, multi-cellular organisms is far from
trivial, requiring stringent additional conditions on planetary platforms. An
attempt is made to disentangle the necessary steps leading from a selection of
universes out of a hypothetical multiverse to the existence of life and of
complex life. It is suggested that what is currently called the "anthropic
principle" should instead be named the "prebiotic principle."Comment: 6 pages, RevTeX, in press, Int. J. Mod. Phys.
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