251 research outputs found
A simple stochastic model for the dynamics of condensation
We consider the dynamics of a model introduced recently by Bialas, Burda and
Johnston. At equilibrium the model exhibits a transition between a fluid and a
condensed phase. For long evolution times the dynamics of condensation
possesses a scaling regime that we study by analytical and numerical means. We
determine the scaling form of the occupation number probabilities. The
behaviour of the two-time correlations of the energy demonstrates that aging
takes place in the condensed phase, while it does not in the fluid phase.Comment: 8 pages, plain tex, 2 figure
Structure of the stationary state of the asymmetric target process
We introduce a novel migration process, the target process. This process is
dual to the zero-range process (ZRP) in the sense that, while for the ZRP the
rate of transfer of a particle only depends on the occupation of the departure
site, it only depends on the occupation of the arrival site for the target
process. More precisely, duality associates to a given ZRP a unique target
process, and vice-versa. If the dynamics is symmetric, i.e., in the absence of
a bias, both processes have the same stationary-state product measure. In this
work we focus our interest on the situation where the latter measure exhibits a
continuous condensation transition at some finite critical density ,
irrespective of the dimensionality. The novelty comes from the case of
asymmetric dynamics, where the target process has a nontrivial fluctuating
stationary state, whose characteristics depend on the dimensionality. In one
dimension, the system remains homogeneous at any finite density. An alternating
scenario however prevails in the high-density regime: typical configurations
consist of long alternating sequences of highly occupied and less occupied
sites. The local density of the latter is equal to and their
occupation distribution is critical. In dimension two and above, the asymmetric
target process exhibits a phase transition at a threshold density much
larger than . The system is homogeneous at any density below ,
whereas for higher densities it exhibits an extended condensate elongated along
the direction of the mean current, on top of a critical background with density
.Comment: 30 pages, 16 figure
Nonequilibrium phase transition in a non integrable zero-range process
The present work is an endeavour to determine analytically features of the
stationary measure of a non-integrable zero-range process, and to investigate
the possible existence of phase transitions for such a nonequilibrium model.
The rates defining the model do not satisfy the constraints necessary for the
stationary measure to be a product measure. Even in the absence of a drive,
detailed balance with respect to this measure is violated. Analytical and
numerical investigations on the complete graph demonstrate the existence of a
first-order phase transition between a fluid phase and a condensed phase, where
a single site has macroscopic occupation. The transition is sudden from an
imbalanced fluid where both species have densities larger than the critical
density, to a critical neutral fluid and an imbalanced condensate
Dynamics of the condensate in zero-range processes
For stochastic processes leading to condensation, the condensate, once it is
formed, performs an ergodic stationary-state motion over the system. We analyse
this motion, and especially its characteristic time, for zero-range processes.
The characteristic time is found to grow with the system size much faster than
the diffusive timescale, but not exponentially fast. This holds both in the
mean-field geometry and on finite-dimensional lattices. In the generic
situation where the critical mass distribution follows a power law, the
characteristic time grows as a power of the system size.Comment: 27 pages, 7 figures. Minor changes and updates performe
Nonequilibrium dynamics of urn models
Dynamical urn models, such as the Ehrenfest model, have played an important
role in the early days of statistical mechanics. Dynamical many-urn models
generalize the former models in two respects: the number of urns is
macroscopic, and thermal effects are included. These many-urn models are
exactly solvable in the mean-field geometry. They allow analytical
investigations of the characteristic features of nonequilibrium dynamics
referred to as aging, including the scaling of correlation and response
functions in the two-time plane and the violation of the
fluctuation-dissipation theorem. This review paper contains a general
presentation of these models, as well as a more detailed description of two
dynamical urn models, the backgammon model and the zeta urn model.Comment: 15 pages. Contribution to the Proceedings of the ESF SPHINX meeting
`Glassy behaviour of kinetically constrained models' (Barcelona, March 22-25,
2001). To appear in a special issue of J. Phys. Cond. Mat
Condensation phenomena with distinguishable particles
We study real-space condensation phenomena in a type of classical stochastic
processes (site-particle system), such as zero-range processes and urn models.
We here study a stochastic process in the Ehrenfest class, i.e., particles in a
site are distinguishable. In terms of the statistical mechanical analogue, the
Ehrenfest class obeys the Maxwell-Boltzmann statistics. We analytically clarify
conditions for condensation phenomena in disordered cases in the Ehrenfest
class. In addition, we discuss the preferential urn model as an example of the
disordered urn model. It becomes clear that the quenched disorder property
plays an important role in the occurrence of the condensation phenomenon in the
preferential urn model. It is revealed that the preferential urn model shows
three types of condensation depending on the disorder parameters.Comment: 7 pages, 4 figure
Condensation and coexistence in a two-species driven model
Condensation transition in two-species driven systems in a ring geometry is
studied in the case where current-density relation of a domain of particles
exhibits two degenerate maxima. It is found that the two maximal current phases
coexist both in the fluctuating domains of the fluid and in the condensate,
when it exists. This has a profound effect on the steady state properties of
the model. In particular, phase separation becomes more favorable, as compared
with the case of a single maximum in the current-density relation. Moreover, a
selection mechanism imposes equal currents flowing out of the condensate,
resulting in a neutral fluid even when the total number of particles of the two
species are not equal. In this case the particle imbalance shows up only in the
condensate
Scaling of the magnetic linear response in phase-ordering kinetics
The scaling of the thermoremanent magnetization and of the dissipative part
of the non-equilibrium magnetic susceptibility is analysed as a function of the
waiting-time for a simple ferromagnet undergoing phase-ordering kinetics
after a quench into the ferromagnetically ordered phase. Their scaling forms
describe the cross-over between two power-law regimes governed by the
non-equilibrium exponents and , respectively. A relation
between , the dynamical exponent and the equilibrium exponent is
derived from scaling arguments. Explicit tests in the Glauber-Ising model and
the kinetic spherical model are presented.Comment: 7 pages, 2 figures included, needs epl.cls, version to appear in
Europhys. Let
Nonequilibrium critical dynamics of ferromagnetic spin systems
We use simple models (the Ising model in one and two dimensions, and the
spherical model in arbitrary dimension) to put to the test some recent ideas on
the slow dynamics of nonequilibrium systems. In this review the focus is on the
temporal evolution of two-time quantities and on the violation of the
fluctuation-dissipation theorem, with special emphasis given to nonequilibrium
critical dynamics.Comment: 11 pages, 2 figures.Contribution to the Proceedings of the ESF SPHINX
meeting `Glassy behaviour of kinetically constrained models' (Barcelona,
March 22-25, 2001). To appear in a special issue of J. Phys. Cond. Mat
Irreversible spherical model and its stationary entropy production rate
The nonequilibrium stationary state of an irreversible spherical model is
investigated on hypercubic lattices. The model is defined by Langevin equations
similar to the reversible case, but with asymmetric transition rates. In spite
of being irreversible, we have succeeded in finding an explicit form for the
stationary probability distribution, which turns out to be of the
Boltzmann-Gibbs type. This enables one to evaluate the exact form of the
entropy production rate at the stationary state, which is non-zero if the
dynamical rules of the transition rates are asymmetric
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