1,380 research outputs found
Where are the Hedgehogs in Nematics?
In experiments which take a liquid crystal rapidly from the isotropic to the
nematic phase, a dense tangle of defects is formed. In nematics, there are in
principle both line and point defects (``hedgehogs''), but no point defects are
observed until the defect network has coarsened appreciably. In this letter the
expected density of point defects is shown to be extremely low, approximately
per initially correlated domain, as result of the topology
(specifically, the homology) of the order parameter space.Comment: 6 pages, latex, 1 figure (self-unpacking PostScript)
Abelian Higgs Cosmic Strings: Small Scale Structure and Loops
Classical lattice simulations of the Abelian Higgs model are used to
investigate small scale structure and loop distributions in cosmic string
networks. Use of the field theory ensures that the small-scale physics is
captured correctly. The results confirm analytic predictions of Polchinski &
Rocha [1] for the two-point correlation function of the string tangent vector,
with a power law from length scales of order the string core width up to
horizon scale with evidence to suggest that the small scale structure builds up
from small scales. An analysis of the size distribution of string loops gives a
very low number density, of order 1 per horizon volume, in contrast with
Nambu-Goto simulations. Further, our loop distribution function does not
support the detailed analytic predictions for loop production derived by Dubath
et al. [2]. Better agreement to our data is found with a model based on loop
fragmentation [3], coupled with a constant rate of energy loss into massive
radiation. Our results show a strong energy loss mechanism which allows the
string network to scale without gravitational radiation, but which is not due
to the production of string width loops. From evidence of small scale structure
we argue a partial explanation for the scale separation problem of how energy
in the very low frequency modes of the string network is transformed into the
very high frequency modes of gauge and Higgs radiation. We propose a picture of
string network evolution which reconciles the apparent differences between
Nambu-Goto and field theory simulations.Comment: 16 pages, 17 figure
Correlations in Cosmic String Networks
We investigate scaling and correlations of the energy and momentum in an
evolving network of cosmic strings in Minkowski space. These quantities are of
great interest, as they must be understood before accurate predictions for the
power spectra of the perturbations in the matter and radiation in the early
Universe can be made. We argue that Minkowski space provides a reasonable
approximation to a Friedmann background for string dynamics and we use our
results to construct a simple model of the network, in which it is considered
to consist of randomly placed segments moving with random velocities. This
model works well in accounting for features of the two-time correlation
functions, and even better for the power spectra.Comment: 20pp Plain LaTeX, 11 EPS figures, uses epsf.st
Twisted Superconducting Semilocal Strings
A new class of twisted, current carrying, stationary, straight string
solutions having finite energy per unit length is constructed numerically in an
extended Abelian Higgs model with global SU(2) symmetry. The new solutions
correspond to deformations of the embedded Abrikosov-Nielsen-Olesen (ANO)
vortices by a twist -- a relative coordinate dependent phase between the two
Higgs fields. The twist induces a global current flowing through the string,
and the deformed solutions bifurcate with the ANO vortices in the limit of
vanishing current. For each value of the winding number (determining
the magnetic flux through the plane orthogonal to the string) there are
distinct, two-parametric families of solutions. One of the continuously varying
parameters is the twist, or the corresponding current, the other one can be
chosen to be the momentum of the string. For fixed values of the momentum and
twist, the distinct solutions have different energies and can be viewed as
a lowest energy ``fundamental'' string and its ``excitations''
characterized by different values of their ``polarization''. The latter is
defined as the ratio of the angular momentum of the vortex and its momentum. In
their rest frame the twisted vortices have lower energy than the embedded ANO
vortices and could be of considerable importance in various physical systems
(from condensed matter to cosmic strings).Comment: 39 pages, 20 figure
Renormalisation group improvement of scalar field inflation
We study quantum corrections to Friedmann-Robertson-Walker cosmology with a
scalar field under the assumption that the dynamics are subject to
renormalisation group improvement. We use the Bianchi identity to relate the
renormalisation group scale to the scale factor and obtain the improved
cosmological evolution equations. We study the solutions of these equations in
the renormalisation group fixed point regime, obtaining the time-dependence of
the scalar field strength and the Hubble parameter in specific models with
monomial and trinomial quartic scalar field potentials. We find that power-law
inflation can be achieved in the renormalisation group fixed point regime with
the trinomial potential, but not with the monomial one. We study the transition
to the quasi-classical regime, where the quantum corrections to the couplings
become small, and find classical dynamics as an attractor solution for late
times. We show that the solution found in the renormalisation group fixed point
regime is also a cosmological fixed point in the autonomous phase space. We
derive the power spectrum of cosmological perturbations and find that the
scalar power spectrum is exactly scale-invariant and bounded up to arbitrarily
small times, while the tensor perturbations are tilted as appropriate for the
background power-law inflation. We specify conditions for the renormalisation
group fixed point values of the couplings under which the amplitudes of the
cosmological perturbations remain small.Comment: 17 pages; 2 figure
Large Radius Hagedorn Regime in String Gas Cosmology
We calculate the equation of state of a gas of strings at high density in a
large toroidal universe, and use it to determine the cosmological evolution of
background metric and dilaton fields in the entire large radius Hagedorn
regime, (ln S)^{1/d} << R << S^{1/d} (with S the total entropy). The pressure
in this regime is not vanishing but of O(1), while the equation of state is
proportional to volume, which makes our solutions significantly different from
previously published approximate solutions. For example, we are able to
calculate the duration of the high-density "Hagedorn" phase, which increases
exponentially with increasing entropy, S. We go on to discuss the difficulties
of the scenario, quantifying the problems of establishing thermal equilibrium
and producing a large but not too weakly-coupled universe.Comment: 12 pages, 4 figures, more details presented in string thermodynamics
section, to be published in Physical Review
Defect Production in Slow First Order Phase Transitions
We study the formation of vortices in a U(1) gauge theory following a
first-order transition proceeding by bubble nucleation, in particular the
effect of a low velocity of expansion of the bubble walls. To do this, we use a
two-dimensional model in which bubbles are nucleated at random points in a
plane and at random times and then expand at some velocity .
Within each bubble, the phase angle is assigned one of three discrete values.
When bubbles collide, magnetic `fluxons' appear: if the phases are different, a
fluxon--anti-fluxon pair is formed. These fluxons are eventually trapped in
three-bubble collisions when they may annihilate or form quantized vortices. We
study in particular the effect of changing the bubble expansion speed on the
vortex density and the extent of vortex--anti-vortex correlation.Comment: 13 pages, RevTeX, 15 uuencoded postscript figure
Covariant Closed String Coherent States
We give the first construction of covariant coherent closed string states,
which may be identified with fundamental cosmic strings. We outline the
requirements for a string state to describe a cosmic string, and using DDF
operators provide an explicit and simple map that relates three different
descriptions: classical strings, lightcone gauge quantum states and covariant
vertex operators. The naive construction leads to covariant vertex operators
whose existence requires a lightlike compactification of spacetime. When the
lightlike compactified states in the underlying Hilbert space are projected out
the resulting coherent states have a classical interpretation and are in
one-to-one correspondence with arbitrary classical closed string loops.Comment: 4 page
Defect formation and local gauge invariance
We propose a new mechanism for formation of topological defects in a U(1)
model with a local gauge symmetry. This mechanism leads to definite
predictions, which are qualitatively different from those of the Kibble-Zurek
mechanism of global theories. We confirm these predictions in numerical
simulations, and they can also be tested in superconductor experiments. We
believe that the mechanism generalizes to more complicated theories.Comment: REVTeX, 4 pages, 2 figures. The explicit form of the Hamiltonian and
the equations of motion added. To appear in PRL (http://prl.aps.org/
- …