539 research outputs found
Stochastic field evolution of disoriented chiral condensates
I present a summary of recent work \cite{BRS} where we describe the
time-evolution of a region of disoriented chiral condensate via Langevin field
equations for the linear model. We analyze the model in equilibrium,
paying attention to subtracting ultraviolet divergent classical terms and
replacing them by their finite quantum counterparts. We use results from
lattice gauge theory and chiral perturbation theory to fix nonuniversal
constants. The result is a ultraviolet cutoff independent theory that
reproduces quantitatively the expected equilibrium behavior of pion and
quantum fields. We also estimate the viscosity , which
controls the dynamical timescale in the Langevin equation, so that the near
equilibrium dynamical response agrees with theoretical expectations.Comment: 3 pages, 3 figures, contribution to the proceedings of Lattice0
Patchiness and Demographic Noise in Three Ecological Examples
Understanding the causes and effects of spatial aggregation is one of the
most fundamental problems in ecology. Aggregation is an emergent phenomenon
arising from the interactions between the individuals of the population, able
to sense only -at most- local densities of their cohorts. Thus, taking into
account the individual-level interactions and fluctuations is essential to
reach a correct description of the population. Classic deterministic equations
are suitable to describe some aspects of the population, but leave out features
related to the stochasticity inherent to the discreteness of the individuals.
Stochastic equations for the population do account for these
fluctuation-generated effects by means of demographic noise terms but, owing to
their complexity, they can be difficult (or, at times, impossible) to deal
with. Even when they can be written in a simple form, they are still difficult
to numerically integrate due to the presence of the "square-root" intrinsic
noise. In this paper, we discuss a simple way to add the effect of demographic
stochasticity to three classic, deterministic ecological examples where
aggregation plays an important role. We study the resulting equations using a
recently-introduced integration scheme especially devised to integrate
numerically stochastic equations with demographic noise. Aimed at scrutinizing
the ability of these stochastic examples to show aggregation, we find that the
three systems not only show patchy configurations, but also undergo a phase
transition belonging to the directed percolation universality class.Comment: 20 pages, 5 figures. To appear in J. Stat. Phy
Langevin Evolution of Disoriented Chiral Condensate
As the matter produced in a relativistic heavy ion collision cools through
the QCD phase transition, the dynamical evolution of the chiral condensate will
be driven out of thermal equilibrium. As a prelude to analyzing this evolution,
and in particular as a prelude to learning how rapid the cooling must be in
order for significant deviations from equilibrium to develop, we present a
detailed analysis of the time-evolution of an idealized region of disoriented
chiral condensate. We set up a Langevin field equation which can describe the
evolution of these (or more realistic) linear sigma model configurations in
contact with a heat bath representing the presence of other shorter wavelength
degrees of freedom. We first analyze the model in equilibrium, paying
particular attention to subtracting ultraviolet divergent classical terms and
replacing them by their finite quantum counterparts. We use known results from
lattice gauge theory and chiral perturbation theory to fix nonuniversal
constants. The result is a theory which is ultraviolet cutoff independent and
that reproduces quantitatively the expected equilibrium behavior of the quantum
field theory of pions and sigma fields over a wide range of temperatures.
Finally, we estimate the viscosity , which controls the dynamical
timescale in the Langevin equation, by requiring that the timescale for DCC
decay agrees with previous calculations. The resulting is larger than
that found perturbatively. We also determine the temperature below which the
classical field Langevin equation ceases to be a good model for the quantum
field dynamics.Comment: 19 pages, 7 figures, uses RevTex; v2 very small change to the caption
of Fig.7. Version to appear in Nucl. phys.
Current correlators to all orders in the quark masses
The contributions to the coefficient functions of the quark and the mixed
quark-gluon condensate to mesonic correlators are calculated for the first time
to all orders in the quark masses, and to lowest order in the strong coupling
constant. Existing results on the coefficient functions of the unit operator
and the gluon condensate are reviewed. The proper factorization of short- and
long-distance contributions in the operator product expansion is discussed in
detail. It is found that to accomplish this task rigorously the operator
product expansion has to be performed in terms of non-normal-ordered
condensates. The resulting coefficient functions are improved with the help of
the renormalization group. The scale invariant combination of dimension 5
operators, including mixing with the mass operator, which is needed for the
renormalization group improvement, is calculated in the leading order.Comment: 24 pages, LateX file, TUM-T31-21/92, 1 postscript file include
Improved Determination of the Mass of the Light Hybrid Meson From QCD Sum Rules
We calculate the next-to-leading order (NLO) -corrections to the
contributions of the condensates and in the
current-current correlator of the hybrid current
g\barq(x)\gamma_{\nu}iF_{\mu\nu}^aT^aq(x) using the external field method in
Feynman gauge. After incorporating these NLO contributions into the Laplace
sum-rules, the mass of the = light hybrid meson is recalculated
using the QCD sum rule approach. We find that the sum rules exhibit enhanced
stability when the NLO -corrections are included in the sum rule
analysis, resulting in a light hybrid meson mass of approximately 1.6
GeV.Comment: revtex4, 10 pages, 7 eps figures embedded in manuscrip
- âŠ