228 research outputs found

### MOBILITY IN A ONE-DIMENSIONAL DISORDER POTENTIAL

In this article the one-dimensional, overdamped motion of a classical
particle is considered, which is coupled to a thermal bath and is drifting in a
quenched disorder potential. The mobility of the particle is examined as a
function of temperature and driving force acting on the particle. A framework
is presented, which reveals the dependence of mobility on spatial correlations
of the disorder potential. Mobility is then calculated explicitly for new
models of disorder, in particular with spatial correlations. It exhibits
interesting dynamical phenomena. Most markedly, the temperature dependence of
mobility may deviate qualitatively from Arrhenius formula and a localization
transition from zero to finite mobility may occur at finite temperature.
Examples show a suppression of this transition by disorder correlations.Comment: 10 pages, latex, with 3 figures, to be published in Z. Phys.

### Anomalous diffusion, Localization, Aging and Sub-aging effects in trap models at very low temperature

We study in details the dynamics of the one dimensional symmetric trap model,
via a real-space renormalization procedure which becomes exact in the limit of
zero temperature. In this limit, the diffusion front in each sample consists in
two delta peaks, which are completely out of equilibrium with each other. The
statistics of the positions and weights of these delta peaks over the samples
allows to obtain explicit results for all observables in the limit $T \to 0$.
We first compute disorder averages of one-time observables, such as the
diffusion front, the thermal width, the localization parameters, the
two-particle correlation function, and the generating function of thermal
cumulants of the position. We then study aging and sub-aging effects : our
approach reproduces very simply the two different aging exponents and yields
explicit forms for scaling functions of the various two-time correlations. We
also extend the RSRG method to include systematic corrections to the previous
zero temperature procedure via a series expansion in $T$. We then consider the
generalized trap model with parameter $\alpha \in [0,1]$ and obtain that the
large scale effective model at low temperature does not depend on $\alpha$ in
any dimension, so that the only observables sensitive to $\alpha$ are those
that measure the `local persistence', such as the probability to remain exactly
in the same trap during a time interval. Finally, we extend our approach at a
scaling level for the trap model in $d=2$ and obtain the two relevant time
scales for aging properties.Comment: 33 pages, 3 eps figure

### Non-linear Response of the trap model in the aging regime : Exact results in the strong disorder limit

We study the dynamics of the one dimensional disordered trap model presenting
a broad distribution of trapping times $p(\tau) \sim 1/\tau^{1+\mu}$, when an
external force is applied from the very beginning at $t=0$, or only after a
waiting time $t_w$, in the linear as well as in the non-linear response regime.
Using a real-space renormalization procedure that becomes exact in the limit of
strong disorder $\mu \to 0$, we obtain explicit results for many observables,
such as the diffusion front, the mean position, the thermal width, the
localization parameters and the two-particle correlation function. In
particular, the scaling functions for these observables give access to the
complete interpolation between the unbiased case and the directed case.
Finally, we discuss in details the various regimes that exist for the averaged
position in terms of the two times and the external field.Comment: 27 pages, 1 eps figur

### Anomalous diffusion in random media of any dimensionality

We show, through physical arguments and a renormalization group analysis, that in the presence of long-range correlated random forces, diffusions is anomalous in any dimension. We obtain in general surdiffusive behaviours, except when the random force is the gradient of a potential. In this last situation, with either short or long-range correlations, a subdiffusive behaviour with a disorder dependent exponent is found in the upper critical case (D = 2 for short-range correlations). This is because the β-function vanishes, which is explicitly proven at all orders of the perturbation theory. Apart from this case, a potential force is expected to lead to logarithmic diffusion (1/f noise), as suggested by simple arguments

### Corrections to the Central Limit Theorem for Heavy-Tailed Probability Densities

Classical Edgeworth expansions provide asymptotic correction terms to the
Central Limit Theorem (CLT) up to an order that depends on the number of
moments available. In this paper, we provide subsequent correction terms beyond
those given by a standard Edgeworth expansion in the general case of regularly
varying distributions with diverging moments (beyond the second). The
subsequent terms can be expressed in a simple closed form in terms of certain
special functions (Dawson's integral and parabolic cylinder functions), and
there are qualitative differences depending on whether the number of moments
available is even, odd or not an integer, and whether the distributions are
symmetric or not. If the increments have an even number of moments, then
additional logarithmic corrections must also be incorporated in the expansion
parameter. An interesting feature of our correction terms for the CLT is that
they become dominant outside the central region and blend naturally with known
large-deviation asymptotics when these are applied formally to the spatial
scales of the CLT

### Jamming and Stress Propagation in Particulate Matter

We present simple models of particulate materials whose mechanical integrity
arises from a jamming process. We argue that such media are generically
"fragile", that is, they are unable to support certain types of incremental
loading without plastic rearrangement. In such models, fragility is naturally
linked to the marginal stability of force chain networks (granular skeletons)
within the material. Fragile matter exhibits novel mechanical responses that
may be relevant to both jammed colloids and cohesionless assemblies of poured,
rigid grains.Comment: LATEX, 3 Figures, elsart.cls style file, 11 page

### Elastic Theory of pinned flux lattices

The pinning of flux lattices by weak impurity disorder is studied in the
absence of free dislocations using both the gaussian variational method and, to
$O(\epsilon=4-d)$, the functional renormalization group. We find universal
logarithmic growth of displacements for $2<d<4$: $\overline{\langle u(x)-u(0)
\rangle ^2}\sim A_d \log|x|$ and persistence of algebraic quasi-long range
translational order. When the two methods can be compared they agree within
$10\%$ on the value of $A_d$. We compute the function describing the crossover
between the ``random manifold'' regime and the logarithmic regime. This
crossover should be observable in present decoration experiments.Comment: 12 pages, Revtex 3.

### Wealth distribution in an ancient Egyptian society

Modern excavations yielded a distribution of the house areas in the ancient
Egyptian city Akhetaten, which was populated for a short period during the 14th
century BC. Assuming that the house area is a measure of the wealth of its
inhabitants allows us to make a comparison of the wealth distributions in
ancient and modern societies

### Do investors trade too much?:A laboratory experiment

We run an experiment to investigate the emergence of excess and synchronised trading activity leading to market crashes. Although the environment clearly favours a buy-and-hold strategy, we observe that subjects trade too much, which is detrimental to their wealth given the implemented market impact (known to them). We find that preference for risk leads to higher activity rates and that price expectations are fully consistent with subjects\u2019 actions. In particular, trading subjects try to make profits by playing a buy low, sell high strategy. Finally, we do not detect crashes driven by collective panic, but rather a weak but significant synchronisation of buy activity

### Coupled non-equilibrium growth equations: Self-consistent mode coupling using vertex renormalization

We find that studying the simplest of the coupled non-equilibrium growth
equations of Barabasi by self-consistent mode coupling requires the use of
dressed vertices. Using the vertex renormalization, we find a roughness
exponent which already in the leading order is quite close to the numerical
value.Comment: 7 pages, 3 figure

- …