541 research outputs found
Critical holes in undercooled wetting layers
The profile of a critical hole in an undercooled wetting layer is determined
by the saddle-point equation of a standard interface Hamiltonian supported by
convenient boundary conditions. It is shown that this saddle-point equation can
be mapped onto an autonomous dynamical system in a three-dimensional phase
space. The corresponding flux has a polynomial form and in general displays
four fixed points, each with different stability properties. On the basis of
this picture we derive the thermodynamic behaviour of critical holes in three
different nucleation regimes of the phase diagram.Comment: 18 pages, LaTeX, 6 figures Postscript, submitted to J. Phys.
Coherent State path-integral simulation of many particle systems
The coherent state path integral formulation of certain many particle systems
allows for their non perturbative study by the techniques of lattice field
theory. In this paper we exploit this strategy by simulating the explicit
example of the diffusion controlled reaction . Our results are
consistent with some renormalization group-based predictions thus clarifying
the continuum limit of the action of the problem.Comment: 20 pages, 4 figures. Minor corrections. Acknowledgement and reference
correcte
Unified Solution of the Expected Maximum of a Random Walk and the Discrete Flux to a Spherical Trap
Two random-walk related problems which have been studied independently in the
past, the expected maximum of a random walker in one dimension and the flux to
a spherical trap of particles undergoing discrete jumps in three dimensions,
are shown to be closely related to each other and are studied using a unified
approach as a solution to a Wiener-Hopf problem. For the flux problem, this
work shows that a constant c = 0.29795219 which appeared in the context of the
boundary extrapolation length, and was previously found only numerically, can
be derived explicitly. The same constant enters in higher-order corrections to
the expected-maximum asymptotics. As a byproduct, we also prove a new universal
result in the context of the flux problem which is an analogue of the Sparre
Andersen theorem proved in the context of the random walker's maximum.Comment: Two figs. Accepted for publication, Journal of Statistical Physic
Kovacs effect and fluctuation-dissipation relations in 1D kinetically constrained models
Strong and fragile glass relaxation behaviours are obtained simply changing
the constraints of the kinetically constrained Ising chain from symmetric to
purely asymmetric. We study the out-of-equilibrium dynamics of those two models
focusing on the Kovacs effect and the fluctuation--dissipation relations. The
Kovacs or memory effect, commonly observed in structural glasses, is present
for both constraints but enhanced with the asymmetric ones. Most surprisingly,
the related fluctuation-dissipation (FD) relations satisfy the FD theorem in
both cases. This result strongly differs from the simple quenching procedure
where the asymmetric model presents strong deviations from the FD theorem.Comment: 13 pages and 7 figures. To be published in J. Phys.
Subdiffusion-limited reactions
We consider the coagulation dynamics A+A -> A and A+A A and the
annihilation dynamics A+A -> 0 for particles moving subdiffusively in one
dimension. This scenario combines the "anomalous kinetics" and "anomalous
diffusion" problems, each of which leads to interesting dynamics separately and
to even more interesting dynamics in combination. Our analysis is based on the
fractional diffusion equation
Exponents appearing in heterogeneous reaction-diffusion models in one dimension
We study the following 1D two-species reaction diffusion model : there is a
small concentration of B-particles with diffusion constant in an
homogenous background of W-particles with diffusion constant ; two
W-particles of the majority species either coagulate ()
or annihilate () with the respective
probabilities and ; a B-particle and a
W-particle annihilate () with probability 1. The
exponent describing the asymptotic time decay of
the minority B-species concentration can be viewed as a generalization of the
exponent of persistent spins in the zero-temperature Glauber dynamics of the 1D
-state Potts model starting from a random initial condition : the
W-particles represent domain walls, and the exponent
characterizes the time decay of the probability that a diffusive "spectator"
does not meet a domain wall up to time . We extend the methods introduced by
Derrida, Hakim and Pasquier ({\em Phys. Rev. Lett.} {\bf 75} 751 (1995); Saclay
preprint T96/013, to appear in {\em J. Stat. Phys.} (1996)) for the problem of
persistent spins, to compute the exponent in perturbation
at first order in for arbitrary and at first order in
for arbitrary .Comment: 29 pages. The three figures are not included, but are available upon
reques
Exactly solvable models through the empty interval method
The most general one dimensional reaction-diffusion model with
nearest-neighbor interactions, which is exactly-solvable through the empty
interval method, has been introduced. Assuming translationally-invariant
initial conditions, the probability that consecutive sites are empty
(), has been exactly obtained. In the thermodynamic limit, the large-time
behavior of the system has also been investigated. Releasing the translational
invariance of the initial conditions, the evolution equation for the
probability that consecutive sites, starting from the site , are empty
() is obtained. In the thermodynamic limit, the large time behavior of
the system is also considered. Finally, the continuum limit of the model is
considered, and the empty-interval probability function is obtained.Comment: 12 pages, LaTeX2
Reaction Kinetics of Clustered Impurities
We study the density of clustered immobile reactants in the
diffusion-controlled single species annihilation. An initial state in which
these impurities occupy a subspace of codimension d' leads to a substantial
enhancement of their survival probability. The Smoluchowski rate theory
suggests that the codimensionality plays a crucial role in determining the long
time behavior. The system undergoes a transition at d'=2. For d'<2, a finite
fraction of the impurities survive: ni(t) ~ ni(infinity)+const x log(t)/t^{1/2}
for d=2 and ni(t) ~ ni(infinity)+const/t^{1/2} for d>2. Above this critical
codimension, d'>=2, the subspace decays indefinitely. At the critical
codimension, inverse logarithmic decay occurs, ni(t) ~ log(t)^{-a(d,d')}. Above
the critical codimension, the decay is algebraic ni(t) ~ t^{-a(d,d')}. In
general, the exponents governing the long time behavior depend on the dimension
as well as the codimension.Comment: 10 pages, late
Decoherent Histories Approach to the Arrival Time Problem
We use the decoherent histories approach to quantum theory to compute the
probability of a non-relativistic particle crossing during an interval of
time. For a system consisting of a single non-relativistic particle, histories
coarse-grained according to whether or not they pass through spacetime regions
are generally not decoherent, except for very special initial states, and thus
probabilities cannot be assigned. Decoherence may, however, be achieved by
coupling the particle to an environment consisting of a set of harmonic
oscillators in a thermal bath. Probabilities for spacetime coarse grainings are
thus calculated by considering restricted density operator propagators of the
quantum Brownian motion model. We also show how to achieve decoherence by
replicating the system times and then projecting onto the number density of
particles that cross during a given time interval, and this gives an
alternative expression for the crossing probability. The latter approach shows
that the relative frequency for histories is approximately decoherent for
sufficiently large , a result related to the Finkelstein-Graham-Hartle
theorem.Comment: 42 pages, plain Te
A Method of Intervals for the Study of Diffusion-Limited Annihilation, A + A --> 0
We introduce a method of intervals for the analysis of diffusion-limited
annihilation, A+A -> 0, on the line. The method leads to manageable diffusion
equations whose interpretation is intuitively clear. As an example, we treat
the following cases: (a) annihilation in the infinite line and in infinite
(discrete) chains; (b) annihilation with input of single particles, adjacent
particle pairs, and particle pairs separated by a given distance; (c)
annihilation, A+A -> 0, along with the birth reaction A -> 3A, on finite rings,
with and without diffusion.Comment: RevTeX, 13 pages, 4 figures, 1 table. References Added, and some
other minor changes, to conform with final for
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