373 research outputs found
Emergence of Complex Spatio-Temporal Behavior in Nonlinear Field Theories
We investigate the emergence of time-dependent nonperturbative configurations
during the evolution of nonlinear scalar field models with symmetric and
asymmetric double-well potentials. Complex spatio-temporal behavior emerges as
the system seeks to establish equipartition after a fast quench. We show that
fast quenches may dramatically modify the decay rate of metastable states in
first order phase transitions. We briefly suggest possible applications
incondensed matter systems and early universe cosmology.Comment: 6 pages, 8 figure
Resonant emergence of global and local spatiotemporal order in a nonlinear field model
We investigate the nonequilibrium evolution of a scalar field in (2+1)
dimensions. The field is set in a double-well potential in contact (open) or
not (closed) with a heat bath. For closed systems, we observe the synchronized
emergence of coherent spatiotemporal configurations, identified with oscillons.
This initial global ordering degenerates into localized order until all
oscillons disappear. We show that the synchronization is driven by resonant
parametric oscillations of the field's zero mode and that local ordering is
only possible outside equipartition. None of these orderings occur for open
systems.Comment: 4 pages, 5 figures, LaTeX, minor corrections to eqs. 1,3,
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
Second order perturbations of a Schwarzschild black hole: inclusion of odd parity perturbations
We consider perturbations of a Schwarzschild black hole that can be of both
even and odd parity, keeping terms up to second order in perturbation theory,
for the axisymmetric case. We develop explicit formulae for the
evolution equations and radiated energies and waveforms using the
Regge-Wheeler-Zerilli approach. This formulation is useful, for instance, for
the treatment in the ``close limit approximation'' of the collision of
counterrotating black holes.Comment: 12 pages RevTe
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
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
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
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.
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
A gravitational memory effect in "boosted" black hole perturbation theory
Black hole perturbation theory, or more generally, perturbation theory on a
Schwarzschild bockground, has been applied in several contexts, but usually
under the simplifying assumption that the ADM momentum vanishes, namely, that
the evolution is carried out and observed in the ``center of momentum frame''.
In this paper we consider some consequences of the inclusion of a non vanishing
ADM momentum in the initial data. We first provide a justification for the
validity of the transformation of the initial data to the ``center of momentum
frame'', and then analyze the effect of this transformation on the
gravitational wave amplitude. The most significant result is the possibility of
a type of gravitational memory effect that appears to have no simple relation
with the well known Christodoulou effect.Comment: REVTexIV, 15 pages, 2 EPS figure
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