5,634 research outputs found
Renormalization Group Study of the A+B->0 Diffusion-Limited Reaction
The diffusion-limited reaction, with equal initial densities
, is studied by means of a field-theoretic renormalization
group formulation of the problem. For dimension an effective theory is
derived, from which the density and correlation functions can be calculated. We
find the density decays in time as a,b \sim C\sqrt{\D}(Dt)^{-d/4} for , with \D = n_0-C^\prime n_0^{d/2} + \dots, where is a universal
constant, and is non-universal. The calculation is extended to the
case of unequal diffusion constants , resulting in a new
amplitude but the same exponent. For a controlled calculation is not
possible, but a heuristic argument is presented that the results above give at
least the leading term in an expansion. Finally, we address
reaction zones formed in the steady-state by opposing currents of and
particles, and derive scaling properties.Comment: 17 pages, REVTeX, 13 compressed figures, included with epsf. Eq.
(6.12) corrected, and a moderate rewriting of the introduction. Accepted for
publication in J. Stat. Phy
Persistence in systems with conserved order parameter
We consider the low-temperature coarsening dynamics of a one-dimensional
Ising ferromagnet with conserved Kawasaki-like dynamics in the domain
representation. Domains diffuse with size-dependent diffusion constant, with . We generalize this model to arbitrary
, and derive an expression for the domain density, with , using a scaling argument. We also
investigate numerically the persistence exponent characterizing the
power-law decay of the number, , of persistent (unflipped) spins at
time , and find where depends on
. We show how the results for and are related to
similar calculations in diffusion-limited cluster-cluster aggregation (DLCA)
where clusters with size-dependent diffusion constant diffuse through an
immobile `empty' phase and aggregate irreversibly on impact. Simulations show
that, while is the same in both models, is different except for
. We also investigate models that interpolate between symmetric
domain diffusion and DLCA.Comment: 9 pages, minor revision
Observation of anomalous spin-state segregation in a trapped ultra-cold vapor
We observe counter-intuitive spin segregation in an inhomogeneous sample of
ultra-cold, non-condensed Rubidium atoms in a magnetic trap. We use spatially
selective microwave spectroscopy to verify a model that accounts for the
differential forces on two internal spin states. In any simple understanding of
the cloud dynamics, the forces are far too small to account for the dramatic
transient spin polarizations observed. The underlying mechanism remains to be
elucidated.Comment: 5 pages, 3 figure
TeV-scale electron Compton scattering in the Randall-Sundrum scenario
The spin-2 graviton excitations in the Randall-Sundrum gravity model provides
a t-channel contribution to electron Compton scattering which competes
favourably with the standard QED contributions. The phenomenological
implications of these contributions to the unpolarized and polarized
cross-sections are evaluated.Comment: 11 pages, 5 figure
Global Persistence Exponent for Critical Dynamics
A `persistence exponent' is defined for nonequilibrium critical
phenomena. It describes the probability, , that the
global order parameter has not changed sign in the time interval following
a quench to the critical point from a disordered state. This exponent is
calculated in mean-field theory, in the limit of the model,
to first order in , and for the 1-d Ising model. Numerical
results are obtained for the 2-d Ising model. We argue that is a new
independent exponent.Comment: 4 pages, revtex, one figur
Nontrivial Exponent for Simple Diffusion
The diffusion equation \partial_t\phi = \nabla^2\phi is considered, with
initial condition \phi( _x_ ,0) a gaussian random variable with zero mean.
Using a simple approximate theory we show that the probability p_n(t_1,t_2)
that \phi( _x_ ,t) [for a given space point _x_ ] changes sign n times between
t_1 and t_2 has the asymptotic form p_n(t_1,t_2) \sim
[\ln(t_2/t_1)]^n(t_1/t_2)^{-\theta}. The exponent \theta has predicted values
0.1203, 0.1862, 0.2358 in dimensions d=1,2,3, in remarkably good agreement with
simulation results.Comment: Minor typos corrected, affecting table of exponents. 4 pages, REVTEX,
1 eps figure. Uses epsf.sty and multicol.st
Coarsening in a Driven Ising Chain with Conserved Dynamics
We study the low-temperature coarsening of an Ising chain subject to
spin-exchange dynamics and a small driving force. This dynamical system reduces
to a domain diffusion process, in which entire domains undergo nearest-neighbor
hopping, except for the shortest domains -- dimers -- which undergo long-range
hopping. This system is characterized by two independent length scales: the
average domain length L(t)~t^{1/2} and the average dimer hopping distance l(t)~
t^{1/4}. As a consequence of these two scales, the density C_k(t) of domains of
length k does not obey scaling. This breakdown of scaling also leads to the
density of short domains decaying as t^{-5/4}, instead of the t^{-3/2} decay
that would arise from pure domain diffusion.Comment: 7 pages, 9 figures, revtex 2-column forma
Unparticle Physics in Single Top Signals
We study the single production of top quarks in and
collisions in the context of unparticle physics through the Flavor Violating
(FV) unparticle vertices and compute the total cross sections for single top
production as functions of scale dimension d_{\U}. We find that among all,
LHC is the most promising facility to probe the unparticle physics via single
top quark production processes.Comment: 14 pages, 10 figure
Unusual Dynamical Scaling in the Spatial Distribution of Persistent Sites in 1D Potts Models
The distribution, n(k,t), of the interval sizes, k, between clusters of
persistent sites in the dynamical evolution of the one-dimensional q-state
Potts model is studied using a combination of numerical simulations, scaling
arguments, and exact analysis. It is shown to have the scaling form n(k,t) =
t^{-2z} f(k/t^z), with z= max(1/2,theta), where theta(q) is the persistence
exponent which characterizes the fraction of sites which have not changed their
state up to time t. When theta > 1/2, the scaling length, t^theta, for the
interval-size distribution is larger than the coarsening length scale, t^{1/2},
that characterizes spatial correlations of the Potts variables.Comment: RevTex, 11 page
Particles Sliding on a Fluctuating Surface: Phase Separation and Power Laws
We study a system of hard-core particles sliding downwards on a fluctuating
one-dimensional surface which is characterized by a dynamical exponent . In
numerical simulations, an initially random particle density is found to coarsen
and obey scaling with a growing length scale . The structure
factor deviates from the Porod law in some cases. The steady state is unusual
in that the density-segregation order parameter shows strong fluctuations. The
two-point correlation function has a scaling form with a cusp at small argument
which we relate to a power law distribution of particle cluster sizes. Exact
results on a related model of surface depths provides insight into the origin
of this behaviour.Comment: 5 pages, 5 Postscript figure
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