35 research outputs found
Time evolution of correlation functions and thermalization
We investigate the time evolution of a classical ensemble of isolated
periodic chains of O(N)-symmetric anharmonic oscillators. Our method is based
on an exact evolution equation for the time dependence of correlation
functions. We discuss its solutions in an approximation which retains all
contributions in next-to-leading order in a 1/N expansion and preserves time
reflection symmetry. We observe effective irreversibility and approximate
thermalization. At large time the system approaches stationary solutions in the
vicinity of, but not identical to, thermal equilibrium. The ensemble therefore
retains some memory of the initial condition beyond the conserved total energy.
Such a behavior with incomplete thermalization is referred to as "mesoscopic
dynamics". It is expected for systems in a small volume. Surprisingly, we find
that the nonthermal asymptotic stationary solutions do not change for large
volume. This raises questions on Boltzmann's conjecture that macroscopic
isolated systems thermalize.Comment: 40 pages, 9 figure
Coarse-Grained Fluctuation Probabilities in the Standard Model and Subcritical Bubbles
We compute systematically the probability for fluctuations of the Higgs
field, averaged over a given spatial scale, to exceed a specified value, in the
Standard Model. For the particular case of interest of averages over one
coherence volume we show that, even in the worst possible case of taking the
one-loop improved effective potential parameters, the probability for the field
to fluctuate from the symmetric to the asymmetric minimum before the latter
becomes stable is very small for Higgs masses of the order of those of the
and bosons, whereas the converse is more likely. As such, metastability
should be satisfied dynamically at the Electroweak phase transition and its
dynamics should therefore proceed by the usual mechanism of bubble nucleation
with subcritical fluctuations playing no particularly relevant role in it.Comment: Latex file, 13 pages. 7 figures, available in compressed form by
anonymous ftp from ftp://euclid.tp.ph.ic.ac.uk/papers/94-5_38.fig Latex and
postscript versions also available at
http://euclid.tp.ph.ic.ac.uk/Papers/index.htm
Static intervortex forces
A point particle approximation to the classical dynamics of well separated
vortices of the abelian Higgs model is developed. A static vortex is
asymptotically identical to a solution of the linearized field theory (a
Klein-Gordon/Proca theory) in the presence of a singular point source at the
vortex centre. It is shown that this source is a composite scalar monopole and
magnetic dipole, and the respective charges are determined numerically for
various values of the coupling constant. The interaction potential of two well
separated vortices is computed by calculating the interaction Lagrangian of two
such point sources in the linear theory. The potential is used to model type II
vortex scattering.Comment: Much shorter (10 pages) published version, new titl
The Hartree ensemble approximation revisited: The "symmetric phase"
The Hartree ensemble approximation is studied in the ``symmetric phase'' of
1+1 dimensional lambda phi^4 theory. In comparison with the ``broken phase''
studied previously, it is shown that the dynamical evolution of observables
such as the particle distribution, energy exchange and auto-correlation
functions, is substantially slower. Approximate thermalization is found only
for relatively large energy densities and couplings.Comment: 17 pages RevTeX, 16 figures, 3 tables, uses amsmath and feynmp.
Extended some sections, reordered Sec.IV, added 3 refs, numerical typo
corrected, published versio
Non Intercommuting Configurations in the Collisions of Type-I Cosmic Strings
It is shown that for small relative angle and kinetic energy two type I
strings can form bound states upon collision instead of the more
familiar intercommuting configuration. The velocity below which this may happen
is estimated as function of the ratio of the coupling constants in the theory,
crossing angle and initial kinetic energy.Comment: 12 pages,REVTEX, Imperial/TP/93-94/3
Dressing Up the Kink
Many quantum field theoretical models possess non-trivial solutions which are
stable for topological reasons. We construct a self-consistent example for a
self-interacting scalar field--the quantum (or dressed) kink--using a two
particle irreducible effective action in the Hartree approximation. This new
solution includes quantum fluctuations determined self-consistently and
nonperturbatively at the 1-loop resummed level and allowed to backreact on the
classical mean-field profile. This dressed kink is static under the familiar
Hartree equations for the time evolution of quantum fields. Because the quantum
fluctuation spectrum is lower lying in the presence of the defect, the quantum
kink has a lower rest energy than its classical counterpart. However its energy
is higher than well-known strict 1-loop results, where backreaction and
fluctuation self-interactions are omitted. We also show that the quantum kink
exists at finite temperature and that its profile broadens as temperature is
increased until it eventually disappears.Comment: 13 pages, latex, 3 eps figures; revised with yet additional
references, minor rewordin
A vortex description of the first-order phase transition in type-I superconductors
Using both analytical arguments and detailed numerical evidence we show that
the first order transition in the type-I 2D Abelian Higgs model can be
understood in terms of the statistical mechanics of vortices, which behave in
this regime as an ensemble of attractive particles. The well-known
instabilities of such ensembles are shown to be connected to the process of
phase nucleation. By characterizing the equation of state for the vortex
ensemble we show that the temperature for the onset of a clustering instability
is in qualitative agreement with the critical temperature. Below this point the
vortex ensemble collapses to a single cluster, which is a non-extensive phase,
and disappears in the absence of net topological charge. The vortex description
provides a detailed mechanism for the first order transition, which applies at
arbitrarily weak type-I and is gauge invariant unlike the usual field-theoretic
considerations, which rely on asymptotically large gauge coupling.Comment: 4 pages, 6 figures, uses RevTex. Additional references added, some
small corrections to the tex
Out-of-equilibrium quantum fields with conserved charge
We study the out-of-equilibrium evolution of an O(2)-invariant scalar field
in which a conserved charge is stored. We apply a loop expansion of the
2-particle irreducible effective action to 3-loop order. Equations of motion
are derived which conserve both total charge and total energy yet allow for the
effects of scattering whereby charge and energy can transfer between modes.
Working in (1+1)-dimensions we solve the equations of motion numerically for a
system knocked out of equilibrium by a sudden temperature quench. We examine
the initial stages of the charge and energy redistribution. This provides a
basis from which we can understand the formation of Bose-Einstein condensates
from first principles.Comment: 11 pages, 5 figures, replacement with improved presentatio
The Ginzburg regime and its effects on topological defect formation
The Ginzburg temperature has historically been proposed as the energy scale
of formation of topological defects at a second order symmetry breaking phase
transition. More recently alternative proposals which compute the time of
formation of defects from the critical dynamics of the system, have been
gaining both theoretical and experimental support. We investigate, using a
canonical model for string formation, how these two pictures compare. In
particular we show that prolonged exposure of a critical field configuration to
the Ginzburg regime results in no substantial suppression of the final density
of defects formed. These results dismiss the recently proposed role of the
Ginzburg regime in explaining the absence of topological defects in 4He
pressure quench experiments.Comment: 8 pages, 5 ps figure
Influence Diffusion in Social Networks under Time Window Constraints
We study a combinatorial model of the spread of influence in networks that
generalizes existing schemata recently proposed in the literature. In our
model, agents change behaviors/opinions on the basis of information collected
from their neighbors in a time interval of bounded size whereas agents are
assumed to have unbounded memory in previously studied scenarios. In our
mathematical framework, one is given a network , an integer value
for each node , and a time window size . The goal is to
determine a small set of nodes (target set) that influences the whole graph.
The spread of influence proceeds in rounds as follows: initially all nodes in
the target set are influenced; subsequently, in each round, any uninfluenced
node becomes influenced if the number of its neighbors that have been
influenced in the previous rounds is greater than or equal to .
We prove that the problem of finding a minimum cardinality target set that
influences the whole network is hard to approximate within a
polylogarithmic factor. On the positive side, we design exact polynomial time
algorithms for paths, rings, trees, and complete graphs.Comment: An extended abstract of a preliminary version of this paper appeared
in: Proceedings of 20th International Colloquium on Structural Information
and Communication Complexity (Sirocco 2013), Lectures Notes in Computer
Science vol. 8179, T. Moscibroda and A.A. Rescigno (Eds.), pp. 141-152, 201