169 research outputs found
Instability of coherent states of a real scalar field
We investigate stability of both localized time-periodic coherent states
(pulsons) and uniformly distributed coherent states (oscillating condensate) of
a real scalar field satisfying the Klein-Gordon equation with a logarithmic
nonlinearity. The linear analysis of time-dependent parts of perturbations
leads to the Hill equation with a singular coefficient. To evaluate the
characteristic exponent we extend the Lindemann-Stieltjes method, usually
applied to the Mathieu and Lame equations, to the case that the periodic
coefficient in the general Hill equation is an unbounded function of time. As a
result, we derive the formula for the characteristic exponent and calculate the
stability-instability chart. Then we analyze the spatial structure of the
perturbations. Using these results we show that the pulsons of any amplitudes,
remaining well-localized objects, lose their coherence with time. This means
that, strictly speaking, all pulsons of the model considered are unstable.
Nevertheless, for the nodeless pulsons the rate of the coherence breaking in
narrow ranges of amplitudes is found to be very small, so that such pulsons can
be long-lived. Further, we use the obtaned stability-instability chart to
examine the Affleck-Dine type condensate. We conclude the oscillating
condensate can decay into an ensemble of the nodeless pulsons.Comment: 11 pages, 8 figures, submitted to Physical Review
Generation of Coherent Structures After Cosmic Inflation
We investigate the nonlinear dynamics of hybrid inflation models, which are
characterized by two real scalar fields interacting quadratically. We start by
solving numerically the coupled Klein-Gordon equations in static Minkowski
spacetime, searching for possible coherent structures. We find long-lived,
localized configurations, which we identify as a new kind of oscillon. We
demonstrate that these two-field oscillons allow for "excited" states with much
longer lifetimes than those found in previous studies of single-field
oscillons. We then solve the coupled field equations in an expanding
Friedmann-Robertson-Walker spacetime, finding that as the field responsible for
inflating the Universe rolls down to oscillate about its minimum, it triggers
the formation of long-lived two-field oscillons, which can contribute up to 20%
of the total energy density of the Universe. We show that these oscillons
emerge for a wide range of parameters consistent with WMAP 7-year data. These
objects contain total energy of about 25*10^20 GeV, localized in a region of
approximate radius 6*10^-26 cm. We argue that these structures could have
played a key role during the reheating of the Universe.Comment: 12 pages, 10 .pdf figures, uses RevTex4; v2: expanded discussion in
section IV, accepted for publication in Phys.Rev. D. Results remain the sam
Some stationary properties of a -ball in arbitrary space dimensions
Introducing new physically motivated ans\"{a}tze, we explore both
analytically and numerically the classical and absolute stabilities of a single
-ball in an arbitrary number of spatial dimensions , working in both the
thin and thick wall limits.Comment: 35 pages, 32 figures; added references, corrected typo
Fractal boundary basins in spherically symmetric theory
Results are presented from numerical simulations of the flat-space nonlinear
Klein-Gordon equa- tion with an asymmetric double-well potential in spherical
symmetry. Exit criteria are defined for the simulations that are used to help
understand the boundaries of the basins of attraction for Gaussian "bubble"
initial data. The first exit criteria, based on the immediate collapse or
expan- sion of bubble radius, is used to observe the departure of the scalar
field from a static intermediate attractor solution. The boundary separating
these two behaviors in parameter space is smooth and demonstrates a
time-scaling law with an exponent that depends on the asymmetry of the
potential. The second exit criteria differentiates between the creation of an
expanding true-vacuum bubble and dispersion of the field leaving the false
vacuum; the boundary separating these basins of attraction is shown to
demonstrate fractal behavior. The basins are defined by the number of bounces
that the field undergoes before inducing a phase transition. A third, hybrid
exit criteria is used to determine the location of the boundary to arbitrary
precision and to characterize the threshold behavior. The possible effects this
behavior might have on cosmological phase transitions are briefly discussed.Comment: 10 pages, 13 figures, 1 movie, resubmitted with additional paragraph.
Matches published versio
Szeg\H{o}-type asymptotics for ray sequences of Frobenius-Pad\'e approximants
Let be a Cauchy transform of a possibly complex-valued Borel
measure and be a system of orthonormal polynomials with
respect to a measure ,
. An -th
Frobenius-Pad\'e approximant to is a rational function ,
, , such that the first
Fourier coefficients of the linear form vanish when the
form is developed into a series with respect to the polynomials . We
investigate the convergence of the Frobenius-Pad\'e approximants to
along ray sequences , , when
and are supported on intervals on the real line and their
Radon-Nikodym derivatives with respect to the arcsine distribution of the
respective interval are holomorphic functions
Long-Lived Time-Dependent Remnants During Cosmological Symmetry Breaking: From Inflation to the Electroweak Scale
Through a detailed numerical investigation in three spatial dimensions, we
demonstrate that long-lived time-dependent field configurations emerge
dynamically during symmetry breaking in an expanding de Sitter spacetime. We
investigate two situations: a single scalar field with a double-well potential
and the bosonic sector of an SU(2) non-Abelian Higgs model. For the single
scalar, we show that large-amplitude oscillon configurations emerge
spontaneously and persist to contribute about 1.2% of the energy density of the
universe. We also show that for a range of parameters, oscillon lifetimes are
enhanced by the expansion and that this effect is a result of parametric
resonance. For the SU(2) case, we see about 4% of the final energy density in
oscillons.Comment: 10 pages, RevTex4, 6 figures; v2: expanded SU(2) model section, added
2 figures, added one section, improved overall presentation and updated
references, accepted for publication in Phys. Rev. D. Results remain the sam
Abelian monopoles in finite temperature lattice SU(2) gluodynamics: first study with improved action
The properties of the thermal Abelian color-magnetic monopoles in the
maximally Abelian gauge are studied in the deconfinement phase of the lattice
SU(2) gluodynamics. To check universality of the monopole properties we employ
the tadpole improved Symanzik action. The simulated annealing algorithm
combined with multiple gauge copies is applied for fixing the maximally Abelian
gauge to avoid effects of Gribov copies. We compute the density, interaction
parameters, thermal mass and chemical potential of the thermal Abelian
monopoles in the temperature range between Tc and 3Tc. In comparison with
earlier findings our results for these quantities are improved either with
respect to effects of Gribov copies or with respect to lattice artifacts.Comment: 11 pages, 14 figures, 5 tables; substantially changed version, title
change
Gauge-invariant truncation scheme for the Schwinger-Dyson equations of QCD
We present a new truncation scheme for the Schwinger-Dyson equations of QCD
that respects gauge invariance at any level of the dressed loop expansion. When
applied to the gluon self-energy, it allows for its non-perturbative treatment
without compromising the transversality of the solution, even when entire sets
of diagrams (most notably the ghost loops) are omitted, or treated
perturbatively.Comment: 9 pages, 2 figure
Finite temperature SU(2) gauge theory: critical coupling and universality class
We examine SU(2) gauge theory in 3+1 dimensions at finite temperature in the
vicinity of critical point. For various lattice sizes in time direction
() we extract high precision values of the inverse critical
coupling and critical values of the 4-th order cumulant of Polyakov loops
(Binder cumulant). We check the universality class of the theory by comparing
the cumulant values to that of the 3D Ising model and find very good agreement.
The Polyakov loop correlators for the indicated lattices are also measured
and the string tension values extracted. The high precision values of critical
coupling and string tension allow us to study the scaling of dimensionless
ratio. The violation of scaling by <10% is observed as the
coupling is varied from weak to strong coupling regime.Comment: 17 pages, 9 figures, minor correction
- …