719 research outputs found
Localization of thermal packets and metastable states in Sinai model
We consider the Sinai model describing a particle diffusing in a 1D random
force field. As shown by Golosov, this model exhibits a strong localization
phenomenon for the thermal packet: the disorder average of the thermal
distribution of the relative distance y=x-m(t), with respect to the
(disorder-dependent) most probable position m(t), converges in the limit of
infinite time towards a distribution P(y). In this paper, we revisit this
question of the localization of the thermal packet. We first generalize the
result of Golosov by computing explicitly the joint asymptotic distribution of
relative position y=x(t)-m(t) and relative energy u=U(x(t))-U(m(t)) for the
thermal packet. Next, we compute in the infinite-time limit the localization
parameters Y_k, representing the disorder-averaged probabilities that k
particles of the thermal packet are at the same place, and the correlation
function C(l) representing the disorder-averaged probability that two particles
of the thermal packet are at a distance l from each other. We moreover prove
that our results for Y_k and C(l) exactly coincide with the thermodynamic limit
of the analog quantities computed for independent particles at equilibrium in a
finite sample of length L. Finally, we discuss the properties of the
finite-time metastable states that are responsible for the localization
phenomenon and compare with the general theory of metastable states in glassy
systems, in particular as a test of the Edwards conjecture.Comment: 17 page
Exactly solvable analogy of small-world networks
We present an exact description of a crossover between two different regimes
of simple analogies of small-world networks. Each of the sites chosen with a
probability from sites of an ordered system defined on a circle is
connected to all other sites selected in such a way. Every link is of a unit
length. Thus, while changes from 0 to 1, an averaged shortest distance
between a pair of sites changes from to .
We find the distribution of the shortest distances and obtain a
scaling form of . In spite of the simplicity of the models
under consideration, the results appear to be surprisingly close to those
obtained numerically for usual small-world networks.Comment: 4 pages with 3 postscript figure
Aging dynamics of non-linear elastic interfaces: the Kardar-Parisi-Zhang equation
In this work, the out-of-equilibrium dynamics of the Kardar-Parisi-Zhang
equation in (1+1) dimensions is studied by means of numerical simulations,
focussing on the two-times evolution of an interface in the absence of any
disordered environment. This work shows that even in this simple case, a rich
aging behavior develops. A multiplicative aging scenario for the two-times
roughness of the system is observed, characterized by the same growth exponent
as in the stationary regime. The analysis permits the identification of the
relevant growing correlation length, accounting for the important scaling
variables in the system. The distribution function of the two-times roughness
is also computed and described in terms of a generalized scaling relation.
These results give good insight into the glassy dynamics of the important case
of a non-linear elastic line in a disordered medium.Comment: 14 pages, 6 figure
Equilibrium and out of equilibrium thermodynamics in supercooled liquids and glasses
We review the inherent structure thermodynamical formalism and the
formulation of an equation of state for liquids in equilibrium based on the
(volume) derivatives of the statistical properties of the potential energy
surface. We also show that, under the hypothesis that during aging the system
explores states associated to equilibrium configurations, it is possible to
generalize the proposed equation of state to out-of-equilibrium conditions. The
proposed formulation is based on the introduction of one additional parameter
which, in the chosen thermodynamic formalism, can be chosen as the local minima
where the slowly relaxing out-of-equilibrium liquid is trapped.Comment: 7 pages, 4 eps figure
The dynamics of thin vibrated granular layers
We describe a series of experiments and computer simulations on vibrated
granular media in a geometry chosen to eliminate gravitationally induced
settling. The system consists of a collection of identical spherical particles
on a horizontal plate vibrating vertically, with or without a confining lid.
Previously reported results are reviewed, including the observation of
homogeneous, disordered liquid-like states, an instability to a `collapse' of
motionless spheres on a perfect hexagonal lattice, and a fluctuating,
hexagonally ordered state. In the presence of a confining lid we see a variety
of solid phases at high densities and relatively high vibration amplitudes,
several of which are reported for the first time in this article. The phase
behavior of the system is closely related to that observed in confined
hard-sphere colloidal suspensions in equilibrium, but with modifications due to
the effects of the forcing and dissipation. We also review measurements of
velocity distributions, which range from Maxwellian to strongly non-Maxwellian
depending on the experimental parameter values. We describe measurements of
spatial velocity correlations that show a clear dependence on the mechanism of
energy injection. We also report new measurements of the velocity
autocorrelation function in the granular layer and show that increased
inelasticity leads to enhanced particle self-diffusion.Comment: 11 pages, 7 figure
The scaling behaviour of screened polyelectrolytes
We present a field-theoretic renormalization group (RG) analysis of a single
flexible, screened polyelectrolyte chain (a Debye-H\"uckel chain) in a polar
solvent. We point out that the Debye-H\"uckel chain may be mapped onto a local
field theory which has the same fixed point as a generalised Potts
model. Systematic analysis of the field theory shows that the system is one
with two interplaying length-scales requiring the calculation of scaling
functions as well as exponents to fully describe its physical behaviour. To
illustrate this, we solve the RG equation and explicitly calculate the
exponents and the mean end-to-end length of the chain.Comment: 6 pages, 1 figure; changed title and slight modification to tex
How glasses explore configuration space
We review a statistical picture of the glassy state derived from the analysis
of the off-equilibrium fluctuation-dissipation relations. We define an
ultra-long time limit where ``one time quantities'' are close to equilibrium
while response and correlation can still display aging.
In this limit it is possible to relate the fluctuation-response relation to
static breaking of ergodicity. The resulting picture suggests that even far
from that limit, the fluctuation-dissipation ratio relates to the rate of
growth of the configurational entropy with free-energy density.Comment: To appear in the proceedings of the "3rd workshop on non-equilibrium
phenomena in supercooled fluids, glasses and amorphous materials" Pisa 22-27
September 200
Long-Range Navigation on Complex Networks using L\'evy Random Walks
We introduce a strategy of navigation in undirected networks, including
regular, random, and complex networks, that is inspired by L\'evy random walks,
generalizing previous navigation rules. We obtained exact expressions for the
stationary probability distribution, the occupation probability, the mean first
passage time, and the average time to reach a node on the network. We found
that the long-range navigation using the L\'evy random walk strategy, compared
with the normal random walk strategy, is more efficient at reducing the time to
cover the network. The dynamical effect of using the L\'evy walk strategy is to
transform a large-world network into a small world. Our exact results provide a
general framework that connects two important fields: L\'evy navigation
strategies and dynamics on complex networks.Comment: 6 pages, 3 figure
Universal law of fractionation for slightly polydisperse systems
By perturbing about a general monodisperse system, we provide a complete description of two-phase equilibria in any system which is slightly polydisperse in some property (e.g., particle size, charge, etc.). We derive a universal law of fractionation which is corroborated by comprehensive experiments on a model colloid-polymer mixture. We furthermore predict that phase separation is an effective method of reducing polydispersity only for systems with a skewed distribution of the polydisperse property
Lack of consensus in social systems
We propose an exactly solvable model for the dynamics of voters in a
two-party system. The opinion formation process is modeled on a random network
of agents. The dynamical nature of interpersonal relations is also reflected in
the model, as the connections in the network evolve with the dynamics of the
voters. In the infinite time limit, an exact solution predicts the emergence of
consensus, for arbitrary initial conditions. However, before consensus is
reached, two different metastable states can persist for exponentially long
times. One state reflects a perfect balancing of opinions, the other reflects a
completely static situation. An estimate of the associated lifetimes suggests
that lack of consensus is typical for large systems.Comment: 4 pages, 6 figures, submitted to Phys. Rev. Let
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