A quantum evaporation effect

A small momentum transfer to a particle interacting with a steep potential barrier gives rise to a quantum evaporation effect which increases the transmission appreciably. This effect results from the unexpectedly large population of quantum states with energies above the height of the barrier. Its characteristic properties are studied and an example of physical system in which it may be observed is given.Comment: 7 pages + 3 figure

Infinite average lifetime of an unstable bright state in the green fluorescent protein

The time evolution of the fluorescence intensity emitted by well-defined ensembles of Green Fluorescent Proteins has been studied by using a standard confocal microscope. In contrast with previous results obtained in single molecule experiments, the photo-bleaching of the ensemble is well described by a model based on Levy statistics. Moreover, this simple theoretical model allows us to obtain information about the energy-scales involved in the aging process.Comment: 4 pages, 4 figure

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

From laser cooling to aging: a unified Levy flight description

Intriguing phenomena such as subrecoil laser cooling of atoms, or aging phenomenon in glasses, have in common that the systems considered do not reach a steady-state during the experiments, although the experimental time scales are very large compared to the microscopic ones. We revisit some standard models describing these phenomena, and reformulate them in a unified framework in terms of lifetimes of the microscopic states of the system. A universal dynamical mechanism emerges, leading to a generic time-dependent distribution of lifetimes, independently of the physical situation considered.Comment: 8 pages, 2 figures; accepted for publication in American Journal of Physic

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

Stochastic Ergodicity Breaking: a Random Walk Approach

The continuous time random walk (CTRW) model exhibits a non-ergodic phase when the average waiting time diverges. Using an analytical approach for the non-biased and the uniformly biased CTRWs, and numerical simulations for the CTRW in a potential field, we obtain the non-ergodic properties of the random walk which show strong deviations from Boltzmann--Gibbs theory. We derive the distribution function of occupation times in a bounded region of space which, in the ergodic phase recovers the Boltzmann--Gibbs theory, while in the non-ergodic phase yields a generalized non-ergodic statistical law.Comment: 5 pages, 3 figure

Quantum coherence generated by interference-induced state selectiveness

The relations between quantum coherence and quantum interference are discussed. A general method for generation of quantum coherence through interference-induced state selection is introduced and then applied to `simple' atomic systems under two-photon transitions, with applications in quantum optics and laser cooling.Comment: 17 pages, 7 figures, to be published in Journal of Modern Optics' special issue on quantum interferenc