121 research outputs found
Directed percolation with a single defect site
In a recent study [arXiv:1011.3254] the contact process with a modified
creation rate at a single site was shown to exhibit a non-universal scaling
behavior with exponents varying with the creation rate at the special site. In
the present work we argue that the survival probability decays according to a
stretched exponential rather than a power law, explaining previous
observations.Comment: 8 pages, 3 figure
Numerical study of a model for non-equilibrium wetting
We revisit the scaling properties of a model for non-equilibrium wetting
[Phys. Rev. Lett. 79, 2710 (1997)], correcting previous estimates of the
critical exponents and providing a complete scaling scheme. Moreover, we
investigate a special point in the phase diagram, where the model exhibits a
roughening transition related to directed percolation. We argue that in the
vicinity of this point evaporation from the middle of plateaus can be
interpreted as an external field in the language of directed percolation. This
analogy allows us to compute the crossover exponent and to predict the form of
the phase transition line close to its terminal point.Comment: 8 pages, 8 figure
Arcsine Laws in Stochastic Thermodynamics
We show that the fraction of time a thermodynamic current spends above its
average value follows the arcsine law, a prominent result obtained by L\'evy
for Brownian motion. Stochastic currents with long streaks above or below their
average are much more likely than those that spend similar fractions of time
above and below their average. Our result is confirmed with experimental data
from a Brownian Carnot engine. We also conjecture that two other random times
associated with currents obey the arcsine law: the time a current reaches its
maximum value and the last time a current crosses its average value. These
results apply to, inter alia, molecular motors, quantum dots and colloidal
systems.Comment: 11 pages, 11 figure
Boundary-induced nonequilibrium phase transition into an absorbing state
We demonstrate that absorbing phase transitions in one dimension may be
induced by the dynamics of a single site. As an example we consider a
one-dimensional model of diffusing particles, where a single site at the
boundary evolves according to the dynamics of a contact process. As the rate
for offspring production at this site is varied, the model exhibits a phase
transition from a fluctuating active phase into an absorbing state. The
universal properties of the transition are analyzed by numerical simulations
and approximation techniques.Comment: 4 pages, 4 figures; minor change
Entropy production and fluctuation relations for a KPZ interface
We study entropy production and fluctuation relations in the restricted
solid-on-solid growth model, which is a microscopic realization of the KPZ
equation. Solving the one dimensional model exactly on a particular line of the
phase diagram we demonstrate that entropy production quantifies the distance
from equilibrium. Moreover, as an example of a physically relevant current
different from the entropy, we study the symmetry of the large deviation
function associated with the interface height. In a special case of a system of
length L=4 we find that the probability distribution of the variation of height
has a symmetric large deviation function, displaying a symmetry different from
the Gallavotti-Cohen symmetry.Comment: 21 pages, 5 figure
Finite size effects in nonequilibrium wetting
Models with a nonequilibrium wetting transition display a transition also in
finite systems. This is different from nonequilibrium phase transitions into an
absorbing state, where the stationary state is the absorbing one for any value
of the control parameter in a finite system. In this paper, we study what kind
of transition takes place in finite systems of nonequilibrium wetting models.
By solving exactly a microscopic model with three and four sites and performing
numerical simulations we show that the phase transition taking place in a
finite system is characterized by the average interface height performing a
random walk at criticality and does not discriminate between the bounded-KPZ
classes and the bounded-EW class. We also study the finite size scaling of the
bKPZ universality classes, showing that it presents peculiar features in
comparison with other universality classes of nonequilibrium phase transitions.Comment: 14 pages, 6figures, major change
Rate Equations and Scaling in Pulsed Laser Deposition
We study a simplified model for pulsed laser deposition [Phys. Rev. Lett.
{\bf 87}, 135701 (2001)] by rate equations. We consider a set of equations,
where islands are assumed to be point-like, as well as an improved one that
takes the size of the islands into account. The first set of equations is
solved exactly but its predictive power is restricted to a few pulses. The
improved set of equations is integrated numerically, is in excellent agreement
with simulations, and fully accounts for the crossover from continuous to
pulsed deposition. Moreover, we analyze the scaling of the nucleation density
and show numerical results indicating that a previously observed logarithmic
scaling does not apply.Comment: 8 pages, 9 figure
Simplest nonequilibrium phase transition into an absorbing state
We study in further detail particle models displaying a boundary-induced
absorbing state phase transition [Phys. Rev. E. {\bf 65}, 046104 (2002) and
Phys. Rev. Lett. {\bf 100}, 165701 (2008)] . These are one-dimensional systems
consisting of a single site (the boundary) where creation and annihilation of
particles occur and a bulk where particles move diffusively. We study different
versions of these models, and confirm that, except for one exactly solvable
bosonic variant exhibiting a discontinuous transition and trivial exponents,
all the others display non-trivial behavior, with critical exponents differing
from their mean-field values, representing a universality class. Finally, the
relation of these systems with a -dimensional non-Markovian process is
discussed.Comment: 9 pages, 7 figures, minor change
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