300 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
Information-Entropic Measure of Energy-Degenerate Kinks in Two-Field Models
We investigate the existence and properties of kink-like solitons in a class
of models with two interacting scalar fields. In particular, we focus on models
that display both double and single-kink solutions, treatable analytically
using the Bogomol'nyi--Prasad--Sommerfield bound (BPS). Such models are of
interest in applications that include Skyrmions and various
superstring-motivated theories. Exploring a region of parameter space where the
energy for very different spatially-bound configurations is degenerate, we show
that a newly-proposed momentum-space entropic measure called Configurational
Entropy (CE) can distinguish between such energy-degenerate spatial profiles.
This information-theoretic measure of spatial complexity provides a
complementary perspective to situations where strictly energy-based arguments
are inconclusive
Dynamics of Weak First Order Phase Transitions
The dynamics of weak vs. strong first order phase transitions is investigated
numerically for 2+1 dimensional scalar field models. It is argued that the
change from a weak to a strong transition is itself a (second order) phase
transition, with the order parameter being the equilibrium fractional
population difference between the two phases at the critical temperature, and
the control parameter being the coefficient of the cubic coupling in the
free-energy density. The critical point is identified, and a power law
controlling the relaxation dynamics at this point is obtained. Possible
applications are briefly discussed.Comment: 11 pages, 4 figures in uuencoded compressed file (see instructions in
main text), RevTeX, DART-HEP-94/0
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
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
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
What We Know and What We Don't Know About the Universe
I present a non-technical and necessarily biased and incomplete overview of
our present understanding of the physical universe and its constituents,
emphasizing what we have learned from the explosive growth in cosmological and
astrophysical data acquisition and some of the key open questions that remain.
The topics are organized under the labels space, time, and matter. Most
bibliographical references are for the non-expert.Comment: 5 pages, LaTeX. Keynote address at the International Workshop on
Astronomy and Relativistc Astrophysics, October 12-16, Olinda, Brazil. To be
published in the proceedings (Int. J. Mod. Phys. D
Colliding black holes: how far can the close approximation go?
We study the head-on collision of two equal-mass momentarily stationary black
holes, using black hole perturbation theory up to second order. Compared to
first-order results, this significantly improves agreement with numerically
computed waveforms and energy. Much more important, second-order results
correctly indicate the range of validity of perturbation theory. This use of
second-order, to provide ``error bars,'' makes perturbation theory a viable
tool for providing benchmarks for numerical relativity in more generic
collisions and, in some range of collision parameters, for supplying waveform
templates for gravitational wave detection.Comment: 6 pages, RevTeX, 2 figures included with eps
Metastability in Two Dimensions and the Effective Potential
We study analytically and numerically the decay of a metastable phase in
(2+1)-dimensional classical scalar field theory coupled to a heat bath, which
is equivalent to two-dimensional Euclidean quantum field theory at zero
temperature. By a numerical simulation we obtain the nucleation barrier as a
function of the parameters of the potential, and compare it to the theoretical
prediction from the bounce (critical bubble) calculation. We find the
nucleation barrier to be accurately predicted by theory using the bounce
configuration obtained from the tree-level (``classical'') effective action.
Within the range of parameters probed, we found that using the bounce derived
from the one-loop effective action requires an unnaturally large prefactor to
match the lattice results. Deviations from the tree-level prediction are seen
in the regime where loop corrections would be expected to become important.Comment: 13pp, LaTex with Postscript figs, CLNS 93/1202, DART-HEP-93/0
Inhomogeneous nucleation in quark hadron phase transition
The effect of subcritical hadron bubbles on a first-order quark-hadron phase
transition is studied. These subcritical hadron bubbles are created due to
thermal fluctuations, and can introduce a finite amount of phase mixing (quark
phase mixed with hadron phase) even at and above the critical temperature. For
reasonable choices of surface tension and correlation length, as obtained from
the lattice QCD calculations, we show that the amount of phase mixing at the
critical temperature remains below the percolation threshold. Thus, as the
system cools below the critical temperature, the transition proceeds through
the nucleation of critical-size hadron bubbles from a metastable quark-gluon
phase (QGP), within an inhomogeneous background populated by an equilibrium
distribution of subcritical hadron bubbles. The inhomogeneity of the medium
results in a substantial reduction of the nucleation barrier for critical
bubbles. Using the corrected nucleation barrier, we estimate the amount of
supercooling for different parameters controlling the phase transition, and
briefly discuss its implications to cosmology and heavy-ion collisions.Comment: LaTeX, 14 pages with 8 Postscript figures. Discussion added in
introduction and conclusion, Fig. 8 added, few more references added,
Typographical errors corrected. Version to appear in Phys. Rev.
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