480 research outputs found
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
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
Policy Gradients for CVaR-Constrained MDPs
We study a risk-constrained version of the stochastic shortest path (SSP)
problem, where the risk measure considered is Conditional Value-at-Risk (CVaR).
We propose two algorithms that obtain a locally risk-optimal policy by
employing four tools: stochastic approximation, mini batches, policy gradients
and importance sampling. Both the algorithms incorporate a CVaR estimation
procedure, along the lines of Bardou et al. [2009], which in turn is based on
Rockafellar-Uryasev's representation for CVaR and utilize the likelihood ratio
principle for estimating the gradient of the sum of one cost function
(objective of the SSP) and the gradient of the CVaR of the sum of another cost
function (in the constraint of SSP). The algorithms differ in the manner in
which they approximate the CVaR estimates/necessary gradients - the first
algorithm uses stochastic approximation, while the second employ mini-batches
in the spirit of Monte Carlo methods. We establish asymptotic convergence of
both the algorithms. Further, since estimating CVaR is related to rare-event
simulation, we incorporate an importance sampling based variance reduction
scheme into our proposed algorithms
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 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
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.
Generalised extreme value statistics and sum of correlated variables
We show that generalised extreme value statistics -the statistics of the k-th
largest value among a large set of random variables- can be mapped onto a
problem of random sums. This allows us to identify classes of non-identical and
(generally) correlated random variables with a sum distributed according to one
of the three (k-dependent) asymptotic distributions of extreme value
statistics, namely the Gumbel, Frechet and Weibull distributions. These
classes, as well as the limit distributions, are naturally extended to real
values of k, thus providing a clear interpretation to the onset of Gumbel
distributions with non-integer index k in the statistics of global observables.
This is one of the very few known generalisations of the central limit theorem
to non-independent random variables. Finally, in the context of a simple
physical model, we relate the index k to the ratio of the correlation length to
the system size, which remains finite in strongly correlated systems.Comment: To appear in J.Phys.
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
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
Levy distribution in many-particle quantum systems
Levy distribution, previously used to describe complex behavior of classical
systems, is shown to characterize that of quantum many-body systems. Using two
complimentary approaches, the canonical and grand-canonical formalisms, we
discovered that the momentum profile of a Tonks-Girardeau gas, -- a
one-dimensional gas of impenetrable (hard-core) bosons, harmonically
confined on a lattice at finite temperatures, obeys Levy distribution. Finally,
we extend our analysis to different confinement setups and demonstrate that the
tunable Levy distribution properly reproduces momentum profiles in
experimentally accessible regions. Our finding allows for calibration of
complex many-body quantum states by using a unique scaling exponent.Comment: 7 pages, 6 figures, results are generalized, new examples are adde
Reconstructing past flood events from geomorphological and historical data. The Giétro outburst flood in 1818
- …