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 MgB2_2

Recent optical studies in c-axis oriented superconducting MgB$_2$ 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 $\lambda_{\rm tr} \approx 0.15$, in agreement with Tu et al. [tu01]. To the extent that $\lambda_{\rm tr} \approx \lambda$, this disagrees sharply with model calculations [kong01,kortus01,an01], and is far too low to provide the means for $T_c = 39$ 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 $T_c$.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 $n$ 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 $\lambda(x)\sim\ell^{\alpha}/|x|^{1+\alpha}$ ($|x|\gg\ell$), 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 $\sim t^{-3/2}$. 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.