851 research outputs found
High temperature color conductivity at next-to-leading log order
The non-Abelian analog of electrical conductivity at high temperature has
previously been known only at leading logarithmic order: that is, neglecting
effects suppressed only by an inverse logarithm of the gauge coupling. We
calculate the first sub-leading correction. This has immediate application to
improving, to next-to-leading log order, both effective theories of
non-perturbative color dynamics, and calculations of the hot electroweak baryon
number violation rate.Comment: 47 pages, 6+2 figure
Condensation temperature of interacting Bose gases with and without disorder
The momentum-shell renormalization group (RG) is used to study the
condensation of interacting Bose gases without and with disorder. First of all,
for the homogeneous disorder-free Bose gas the interaction-induced shifts in
the critical temperature and chemical potential are determined up to second
order in the scattering length. The approach does not make use of dimensional
reduction and is thus independent of previous derivations. Secondly, the RG is
used together with the replica method to study the interacting Bose gas with
delta-correlated disorder. The flow equations are derived and found to reduce,
in the high-temperature limit, to the RG equations of the classical
Landau-Ginzburg model with random-exchange defects. The random fixed point is
used to calculate the condensation temperature under the combined influence of
particle interactions and disorder.Comment: 7 pages, 2 figure
Non-perturbative dynamics of hot non-Abelian gauge fields: beyond leading log approximation
Many aspects of high-temperature gauge theories, such as the electroweak
baryon number violation rate, color conductivity, and the hard gluon damping
rate, have previously been understood only at leading logarithmic order (that
is, neglecting effects suppressed only by an inverse logarithm of the gauge
coupling). We discuss how to systematically go beyond leading logarithmic order
in the analysis of physical quantities. Specifically, we extend to
next-to-leading-log order (NLLO) the simple leading-log effective theory due to
Bodeker that describes non-perturbative color physics in hot non-Abelian
plasmas. A suitable scaling analysis is used to show that no new operators
enter the effective theory at next-to-leading-log order. However, a NLLO
calculation of the color conductivity is required, and we report the resulting
value. Our NLLO result for the color conductivity can be trivially combined
with previous numerical work by G. Moore to yield a NLLO result for the hot
electroweak baryon number violation rate.Comment: 20 pages, 1 figur
Effect of Microscopic Damage Events on Static and Ballistic Impact Strength of Triaxial Braid Composites
The reliability of impact simulations for aircraft components made with triaxial-braided carbon-fiber composites is currently limited by inadequate material property data and lack of validated material models for analysis. Methods to characterize the material properties used in the analytical models from a systematically obtained set of test data are also lacking. A macroscopic finite element based analytical model to analyze the impact response of these materials has been developed. The stiffness and strength properties utilized in the material model are obtained from a set of quasi-static in-plane tension, compression and shear coupon level tests. Full-field optical strain measurement techniques are applied in the testing, and the results are used to help in characterizing the model. The unit cell of the braided composite is modeled as a series of shell elements, where each element is modeled as a laminated composite. The braided architecture can thus be approximated within the analytical model. The transient dynamic finite element code LS-DYNA is utilized to conduct the finite element simulations, and an internal LS-DYNA constitutive model is utilized in the analysis. Methods to obtain the stiffness and strength properties required by the constitutive model from the available test data are developed. Simulations of quasi-static coupon tests and impact tests of a represented braided composite are conducted. Overall, the developed method shows promise, but improvements that are needed in test and analysis methods for better predictive capability are examined
Stochastic formulation of the renormalization group: supersymmetric structure and topology of the space of couplings
The exact or Wilson renormalization group equations can be formulated as a
functional Fokker-Planck equation in the infinite-dimensional configuration
space of a field theory, suggesting a stochastic process in the space of
couplings. Indeed, the ordinary renormalization group differential equations
can be supplemented with noise, making them into stochastic Langevin equations.
Furthermore, if the renormalization group is a gradient flow, the space of
couplings can be endowed with a supersymmetric structure a la Parisi-Sourlas.
The formulation of the renormalization group as supersymmetric quantum
mechanics is useful for analysing the topology of the space of couplings by
means of Morse theory. We present simple examples with one or two couplings.Comment: 13 pages, based on contribution to "Progress in Supersymmetric
Quantum Mechanics" (Valladolid U.), accepted in Journal of Physics
Large N Quantum Time Evolution Beyond Leading Order
For quantum theories with a classical limit (which includes the large N
limits of typical field theories), we derive a hierarchy of evolution equations
for equal time correlators which systematically incorporate corrections to the
limiting classical evolution. Explicit expressions are given for
next-to-leading order, and next-to-next-to-leading order time evolution. The
large N limit of N-component vector models, and the usual semiclassical limit
of point particle quantum mechanics are used as concrete examples. Our
formulation directly exploits the appropriate group structure which underlies
the construction of suitable coherent states and generates the classical phase
space. We discuss the growth of truncation error with time, and argue that
truncations of the large-N evolution equations are generically expected to be
useful only for times short compared to a ``decoherence'' time which scales
like N^{1/2}.Comment: 36 pages, 2 eps figures, latex, uses revtex, epsfig, float
Rare Events Statistics in Reaction--Diffusion Systems
We develop an efficient method to calculate probabilities of large deviations
from the typical behavior (rare events) in reaction--diffusion systems. The
method is based on a semiclassical treatment of underlying "quantum"
Hamiltonian, encoding the system's evolution. To this end we formulate
corresponding canonical dynamical system and investigate its phase portrait.
The method is presented for a number of pedagogical examples.Comment: 12 pages, 6 figure
Longitudinal subtleties in diffusive Langevin equations for non-Abelian plasmas
Boedeker has recently argued that non-perturbative processes in very high
temperature non-Abelian plasmas (such as electroweak baryon number violation in
the very hot early Universe) can be quantitatively described, to leading
logarithmic accuracy, by a simple diffusive effective theory. Boedeker's
effective theory is intended to describe the long-distance transverse electric
and magnetic fields which are responsible for non-perturbative dynamics. His
effective theory, however, also contains long-wavelength longitudinal electric
fields. We discuss several subtleties in the treatment of longitudinal dynamics
which were not closely examined in Boedeker's original treatment. Somewhat to
our surprise, we find that within its domain of validity Boedeker's effective
theory does correctly describe both longitudinal and transverse fluctuations.
We also show that, as far as the transverse dynamics of interest is concerned,
Boedeker's effective theory could be replaced by a transverse-only theory that
removes the longitudinal dynamics altogether. In the process, we discuss
several interesting aspects of stochastic field theories.Comment: 29 pages, Section III rewritten, other minor change
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