Broad distribution effects in sums of lognormal random variables

The lognormal distribution describing, e.g., exponentials of Gaussian random variables is one of the most common statistical distributions in physics. It can exhibit features of broad distributions that imply qualitative departure from the usual statistical scaling associated to narrow distributions. Approximate formulae are derived for the typical sums of lognormal random variables. The validity of these formulae is numerically checked and the physical consequences, e.g., for the current flowing through small tunnel junctions, are pointed out.Comment: 14 pages, 9 figures. Minor changes + Gini coefficient and 4 refs. adde

Fractional dynamics in the L\'evy quantum kicked rotor

We investigate the quantum kicked rotor in resonance subjected to momentum measurements with a L\'evy waiting time distribution. We find that the system has a sub-ballistic behavior. We obtain an analytical expression for the exponent of the power law of the variance as a function of the characteristic parameter of the L\'evy distribution and connect this anomalous diffusion with a fractional dynamics

Crossover Time in Relative Fluctuations Characterizes the Longest Relaxation Time of Entangled Polymers

In entangled polymer systems, there are several characteristic time scales, such as the entanglement time and the disengagement time. In molecular simulations, the longest relaxation time (the disengagement time) can be determined by the mean square displacement (MSD) of a segment or by the shear relaxation modulus. Here, we propose the relative fluctuation analysis method, which is originally developed for characterizing large fluctuations, to determine the longest relaxation time from the center of mass trajectories of polymer chains (the time-averaged MSDs). Applying the method to simulation data of entangled polymers (by the slip-spring model and the simple reptation model), we provide a clear evidence that the longest relaxation time is estimated as the crossover time in the relative fluctuations.Comment: 17 pages, 9 figures, to appear in J. Chem. Phy

Fractal time random walk and subrecoil laser cooling considered as renewal processes with infinite mean waiting times

There exist important stochastic physical processes involving infinite mean waiting times. The mean divergence has dramatic consequences on the process dynamics. Fractal time random walks, a diffusion process, and subrecoil laser cooling, a concentration process, are two such processes that look qualitatively dissimilar. Yet, a unifying treatment of these two processes, which is the topic of this pedagogic paper, can be developed by combining renewal theory with the generalized central limit theorem. This approach enables to derive without technical difficulties the key physical properties and it emphasizes the role of the behaviour of sums with infinite means.Comment: 9 pages, 7 figures, to appear in the Proceedings of Cargese Summer School on "Chaotic dynamics and transport in classical and quantum systems

Dephasing by a nonstationary classical intermittent noise

We consider a new phenomenological model for a $1/f^{\mu}$ classical intermittent noise and study its effects on the dephasing of a two-level system. Within this model, the evolution of the relative phase between the $|\pm>$ states is described as a continuous time random walk (CTRW). Using renewal theory, we find exact expressions for the dephasing factor and identify the physically relevant various regimes in terms of the coupling to the noise. In particular, we point out the consequences of the non-stationarity and pronounced non-Gaussian features of this noise, including some new anomalous and aging dephasing scenarii.Comment: Submitted to Phys. Rev.

Phase transitions driven by L\'evy stable noise: exact solutions and stability analysis of nonlinear fractional Fokker-Planck equations

Phase transitions and effects of external noise on many body systems are one of the main topics in physics. In mean field coupled nonlinear dynamical stochastic systems driven by Brownian noise, various types of phase transitions including nonequilibrium ones may appear. A Brownian motion is a special case of L\'evy motion and the stochastic process based on the latter is an alternative choice for studying cooperative phenomena in various fields. Recently, fractional Fokker-Planck equations associated with L\'evy noise have attracted much attention and behaviors of systems with double-well potential subjected to L\'evy noise have been studied intensively. However, most of such studies have resorted to numerical computation. We construct an {\it analytically solvable model} to study the occurrence of phase transitions driven by L\'evy stable noise.Comment: submitted to EP

Power-law tail distributions and nonergodicity

We establish an explicit correspondence between ergodicity breaking in a system described by power-law tail distributions and the divergence of the moments of these distributions.Comment: 4 pages, 1 figure, corrected typo

Optical extinction in a single layer of nanorods

We demonstrate that almost 100 % of incident photons can interact with a monolayer of scatterers in a symmetrical environment. Nearly-perfect optical extinction through free-standing transparent nanorod arrays has been measured. The sharp spectral opacity window, in the form of a characteristic Fano resonance, arises from the coherent multiple scattering in the array. In addition, we show that nanorods made of absorbing material exhibit a 25-fold absorption enhancement per unit volume compared to unstructured thin film. These results open new perspectives for light management in high-Q, low volume dielectric nanostructures, with potential applications in optical systems, spectroscopy, and optomechanics

Bardeen-Petterson effect and the disk structure of the Seyfert galaxy NGC 1068

VLBA high spatial resolution observations of the disk structure of the active galactic nucleus NGC 1068 has recently revealed that the kinematics and geometry of this AGN is well characterized by an outer disk of H2O maser emission having a compact milliarcsecond (parsec) scale structure, which is encircling a thin rotating inner disk surrounding a ~10^7 M_\sun compact mass, likely a black hole. A curious feature in this source is the occurrence of a misalignment between the inner and outer parts of the disk, with the galaxy's radio jet being orthogonal to the inner disk. We interpret this peculiar configuration as due to the Bardeen-Petterson effect, a general relativistic effect that warps an initially inclined (to the black hole equator) viscous disk, and drives the angular momentum vector of its inner part into alignment with the rotating black hole spin. We estimate the time-scale for both angular momenta to get aligned as a function the spin parameter of the Kerr black hole. We also reproduce the shape of the parsec and kiloparsec scale jets, assuming a model in which the jet is precessing with a period and aperture angle that decrease exponentially with time, as expected from the Bardeen-Petterson effect.Comment: 12 pages, 3 figures, accepted for publication in The Astrophysical Journa