148 research outputs found

### Towards deterministic equations for Levy walks: the fractional material derivative

Levy walks are random processes with an underlying spatiotemporal coupling.
This coupling penalizes long jumps, and therefore Levy walks give a proper
stochastic description for a particle's motion with broad jump length
distribution. We derive a generalized dynamical formulation for Levy walks in
which the fractional equivalent of the material derivative occurs. Our approach
will be useful for the dynamical formulation of Levy walks in an external force
field or in phase space for which the description in terms of the continuous
time random walk or its corresponding generalized master equation are less well
suited

### Coherent backscattering under conditions of electromagnetically induced transparency

We consider the influence of a resonant control field on weak localization of
light in ultracold atomic ensembles. Both steady-state and pulsed light
excitation are considered. We show that the presence of a control field
essentially changes the type of interference effects which occur under
conditions of multiple scattering. For example, for some scattering
polarization channels the presence of a control field can cause destructive
interference through which the enhancement factor, normally considered to be
greater than one, becomes less than one.Comment: Submitted to Journal of Modern Optics, Special Issue: Proceedings of
PQE 201

### Fractional Diffusion Equation for a Power-Law-Truncated Levy Process

Truncated Levy flights are stochastic processes which display a crossover
from a heavy-tailed Levy behavior to a faster decaying probability distribution
function (pdf). Putting less weight on long flights overcomes the divergence of
the Levy distribution second moment. We introduce a fractional generalization
of the diffusion equation, whose solution defines a process in which a Levy
flight of exponent alpha is truncated by a power-law of exponent 5 - alpha. A
closed form for the characteristic function of the process is derived. The pdf
of the displacement slowly converges to a Gaussian in its central part showing
however a power law far tail. Possible applications are discussed

### Light trapping in high-density ultracold atomic gases for quantum memory applications

High-density and ultracold atomic gases have emerged as promising media for
storage of individual photons for quantum memory applications. In this paper we
provide an overview of our theoretical and experimental efforts in this
direction, with particular attention paid to manipulation of light storage (a)
through complex recurrent optical scattering processes in very high density
gases (b) by an external control field in a characteristic electromagnetically
induced transparency configuration.Comment: Submitted to Journal of Modern Optics, Special 2010 PQE Issu

### On solutions of a class of non-Markovian Fokker-Planck equations

We show that a formal solution of a rather general non-Markovian
Fokker-Planck equation can be represented in a form of an integral
decomposition and thus can be expressed through the solution of the Markovian
equation with the same Fokker-Planck operator. This allows us to classify
memory kernels into safe ones, for which the solution is always a probability
density, and dangerous ones, when this is not guaranteed. The first situation
describes random processes subordinated to a Wiener process, while the second
one typically corresponds to random processes showing a strong ballistic
component. In this case the non-Markovian Fokker-Planck equation is only valid
in a restricted range of parameters, initial and boundary conditions.Comment: A new ref.12 is added and discusse

### Relaxation Properties of Small-World Networks

Recently, Watts and Strogatz introduced the so-called small-world networks in
order to describe systems which combine simultaneously properties of regular
and of random lattices. In this work we study diffusion processes defined on
such structures by considering explicitly the probability for a random walker
to be present at the origin. The results are intermediate between the
corresponding ones for fractals and for Cayley trees.Comment: 16 pages, 6 figure

### Linear Response in Complex Systems: CTRW and the Fractional Fokker-Planck Equations

We consider the linear response of systems modelled by continuous-time random
walks (CTRW) and by fractional Fokker-Planck equations under the influence of
time-dependent external fields. We calculate the corresponding response
functions explicitely. The CTRW curve exhibits aging, i.e. it is not
translationally invariant in the time-domain. This is different from what
happens under fractional Fokker-Planck conditions

### Does strange kinetics imply unusual thermodynamics?

We introduce a fractional Fokker-Planck equation (FFPE) for Levy flights in
the presence of an external field. The equation is derived within the framework
of the subordination of random processes which leads to Levy flights. It is
shown that the coexistence of anomalous transport and a potential displays a
regular exponential relaxation towards the Boltzmann equilibrium distribution.
The properties of the Levy-flight FFPE derived here are compared with earlier
findings for subdiffusive FFPE. The latter is characterized by a
non-exponential Mittag-Leffler relaxation to the Boltzmann distribution. In
both cases, which describe strange kinetics, the Boltzmann equilibrium is
reached and modifications of the Boltzmann thermodynamics are not required

### Quantum deformation of the angular distributions of synchrotron radiation. Emission of particles in the first excited state

The exact expressions for the characteristics of synchrotron radiation of
charged particles in the first excited state are obtained in analytical form
using quantum theory methods. We performed a detailed analysis of the angular
distribution structure of radiation power and its polarization for particles
with spin 0 and 1/2. It is shown that the exact quantum calculations lead to
results that differ substantially from the predictions of classical theory

### Scaling detection in time series: diffusion entropy analysis

The methods currently used to determine the scaling exponent of a complex
dynamic process described by a time series are based on the numerical
evaluation of variance. This means that all of them can be safely applied only
to the case where ordinary statistical properties hold true even if strange
kinetics are involved. We illustrate a method of statistical analysis based on
the Shannon entropy of the diffusion process generated by the time series,
called Diffusion Entropy Analysis (DEA). We adopt artificial Gauss and L\'{e}vy
time series, as prototypes of ordinary and anomalus statistics, respectively,
and we analyse them with the DEA and four ordinary methods of analysis, some of
which are very popular. We show that the DEA determines the correct scaling
exponent even when the statistical properties, as well as the dynamic
properties, are anomalous. The other four methods produce correct results in
the Gauss case but fail to detect the correct scaling in the case of L\'{e}vy
statistics.Comment: 21 pages,10 figures, 1 tabl

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