1,942 research outputs found
Long-Tailed Trapping Times and Levy Flights in a Self-Organized Critical Granular System
We present a continuous time random walk model for the scale-invariant
transport found in a self-organized critical rice pile [Christensen et al.,
Phys. Rev. Lett. 77, 107 (1996)]. From our analytical results it is shown that
the dynamics of the experiment can be explained in terms of L\'evy flights for
the grains and a long-tailed distribution of trapping times. Scaling relations
for the exponents of these distributions are obtained. The predicted
microscopic behavior is confirmed by means of a cellular automaton model.Comment: 4 pages, RevTex, includes 3 PostScript figures, submitted to Phys.
Rev. Let
Transport Properties of Highly Aligned Polymer Light-Emitting-Diodes
We investigate hole transport in polymer light-emitting-diodes in which the
emissive layer is made of liquid-crystalline polymer chains aligned
perpendicular to the direction of transport. Calculations of the current as a
function of time via a random-walk model show excellent qualitative agreement
with experiments conducted on electroluminescent polyfluorene demonstrating
non-dispersive hole transport. The current exhibits a constant plateau as the
charge carriers move with a time-independent drift velocity, followed by a long
tail when they reach the collecting electrode. Variation of the parameters
within the model allows the investigation of the transition from non-dispersive
to dispersive transport in highly aligned polymers. It turns out that large
inter-chain hopping is required for non-dispersive hole transport and that
structural disorder obstructs the propagation of holes through the polymer
film.Comment: 4 pages, 5 figure
Electrical transport and percolation in magnetoresistive manganite / insulating oxide composites: case of La0.7Ca0.3MnO3 / Mn3O4
We report the results of electrical resistivity measurements carried out on
well-sintered La0.7Ca0.3MnO3 / Mn3O4 composite samples with almost constant
composition of the magnetoresistive manganite phase (La0.7Ca0.3MnO3). A
percolation threshold (fc) occurs when the La0.7Ca0.3MnO3 volume fraction is ~
0.19. The dependence of the electrical resistivity as a function of
La0.7Ca0.3MnO3 volume fraction (fLCMO) can be described by percolation-like
phenomenological equations. Fitting the conducting regime (fLCMO > fc) by the
percolation power law returns a critical exponent t value of 2.0 +/- 0.2 at
room temperature and 2.6 +/-0.2 at 5 K. The increase of t is ascribed to the
influence of the grain boundaries on the electrical conduction process at low
temperature.Comment: 7 pages, 3 figures, accepted for publication in Phys. Rev.
Temperature and Field Dependence of the Mobility in Liquid-Crystalline Conjugated Polymer Films
The transport properties of organic light-emitting diodes in which the
emissive layer is composed of conjugated polymers in the liquid-crystalline
phase have been investigated. We have performed simulations of the current
transient response to an illumination pulse via the Monte Carlo approach, and
from the transit times we have extracted the mobility of the charge carriers as
a function of both the electric field and the temperature. The transport
properties of such films are different from their disordered counterparts, with
charge carrier mobilities exhibiting only a weak dependence on both the
electric field and temperature. We show that for spatially ordered polymer
films, this weak dependence arises for thermal energy being comparable to the
energetic disorder, due to the combined effect of the electrostatic and thermal
energies. The inclusion of spatial disorder, on the other hand, does not alter
the qualitative behaviour of the mobility, but results in decreasing its
absolute value.Comment: 9 pages, 8 figures, submitted to Phys. Rev.
Implications of reflectance measurements on the mechanism for superconductivity in MgB
Recent optical studies in c-axis oriented superconducting MgB films
indicate that the electron-phonon coupling is weak [tu01]. We reinforce this
conclusion by examining the raw reflectance data; its frequency dependence is
incompatible with strong electron-phonon scattering. This is further
strengthened by analysis of the real part of the conductivity, and by the
temperature dependence of the effective Drude scattering rate. Using a
realistic electron-phonon spectral shape [kong01], we find , in agreement with Tu et al. [tu01]. To the extent that
, this disagrees sharply with model
calculations [kong01,kortus01,an01], and is far too low to provide the means
for K. A simple model is constructed with coupling to a high
frequency excitation, which is consistent with both the low frequency optical
data and the high .Comment: 4 pages, 4 figure
Levy flights from a continuous-time process
The Levy-flight dynamics can stem from simple random walks in a system whose
operational time (number of steps n) typically grows superlinearly with
physical time t. Thus, this processes is a kind of continuous-time random walks
(CTRW), dual to usual Scher-Montroll model, in which grows sublinearly with
t. The models in which Levy-flights emerge due to a temporal subordination let
easily discuss the response of a random walker to a weak outer force, which is
shown to be nonlinear. On the other hand, the relaxation of en ensemble of such
walkers in a harmonic potential follows a simple exponential pattern and leads
to a normal Boltzmann distribution. The mixed models, describing normal CTRW in
superlinear operational time and Levy-flights under the operational time of
subdiffusive CTRW lead to paradoxical diffusive behavior, similar to the one
found in transport on polymer chains. The relaxation to the Boltzmann
distribution in such models is slow and asymptotically follows a power-law
Monte-Carlo simulations of the recombination dynamics in porous silicon
A simple lattice model describing the recombination dynamics in visible light
emitting porous Silicon is presented. In the model, each occupied lattice site
represents a Si crystal of nanometer size. The disordered structure of porous
Silicon is modeled by modified random percolation networks in two and three
dimensions. Both correlated (excitons) and uncorrelated electron-hole pairs
have been studied. Radiative and non-radiative processes as well as hopping
between nearest neighbor occupied sites are taken into account. By means of
extensive Monte-Carlo simulations, we show that the recombination dynamics in
porous Silicon is due to a dispersive diffusion of excitons in a disordered
arrangement of interconnected Si quantum dots. The simulated luminescence decay
for the excitons shows a stretched exponential lineshape while for uncorrelated
electron-hole pairs a power law decay is suggested. Our results successfully
account for the recombination dynamics recently observed in the experiments.
The present model is a prototype for a larger class of models describing
diffusion of particles in a complex disordered system.Comment: 33 pages, RevTeX, 19 figures available on request to
[email protected]
A continuous time random walk model for financial distributions
We apply the formalism of the continuous time random walk to the study of
financial data. The entire distribution of prices can be obtained once two
auxiliary densities are known. These are the probability densities for the
pausing time between successive jumps and the corresponding probability density
for the magnitude of a jump. We have applied the formalism to data on the US
dollar/Deutsche Mark future exchange, finding good agreement between theory and
the observed data.Comment: 14 pages, 5 figures, revtex4, submitted for publicatio
First passage and arrival time densities for L\'evy flights and the failure of the method of images
We discuss the first passage time problem in the semi-infinite interval, for
homogeneous stochastic Markov processes with L{\'e}vy stable jump length
distributions (),
namely, L{\'e}vy flights (LFs). In particular, we demonstrate that the method
of images leads to a result, which violates a theorem due to Sparre Andersen,
according to which an arbitrary continuous and symmetric jump length
distribution produces a first passage time density (FPTD) governed by the
universal long-time decay . Conversely, we show that for LFs the
direct definition known from Gaussian processes in fact defines the probability
density of first arrival, which for LFs differs from the FPTD. Our findings are
corroborated by numerical results.Comment: 8 pages, 3 figures, iopart.cls style, accepted to J. Phys. A (Lett
Levy flights in quenched random force fields
Levy flights, characterized by the microscopic step index f, are for f<2 (the
case of rare events) considered in short range and long range quenched random
force fields with arbitrary vector character to first loop order in an
expansion about the critical dimension 2f-2 in the short range case and the
critical fall-off exponent 2f-2 in the long range case. By means of a dynamic
renormalization group analysis based on the momentum shell integration method,
we determine flows, fixed point, and the associated scaling properties for the
probability distribution and the frequency and wave number dependent diffusion
coefficient. Unlike the case of ordinary Brownian motion in a quenched force
field characterized by a single critical dimension or fall-off exponent d=2,
two critical dimensions appear in the Levy case. A critical dimension (or
fall-off exponent) d=f below which the diffusion coefficient exhibits anomalous
scaling behavior, i.e, algebraic spatial behavior and long time tails, and a
critical dimension (or fall-off exponent) d=2f-2 below which the force
correlations characterized by a non trivial fixed point become relevant. As a
general result we find in all cases that the dynamic exponent z, characterizing
the mean square displacement, locks onto the Levy index f, independent of
dimension and independent of the presence of weak quenched disorder.Comment: 27 pages, Revtex file, 17 figures in ps format attached, submitted to
Phys. Rev.
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