120 research outputs found
Multiplicative processes and power laws
[Takayasu et al., Phys. Rev.Lett. 79, 966 (1997)] revisited the question of
stochastic processes with multiplicative noise, which have been studied in
several different contexts over the past decades. We focus on the regime, found
for a generic set of control parameters, in which stochastic processes with
multiplicative noise produce intermittency of a special kind, characterized by
a power law probability density distribution. We briefly explain the physical
mechanism leading to a power law pdf and provide a list of references for these
results dating back from a quarter of century. We explain how the formulation
in terms of the characteristic function developed by Takayasu et al. can be
extended to exponents , which explains the ``reason of the lucky
coincidence''. The multidimensional generalization of (\ref{eq1}) and the
available results are briefly summarized. The discovery of stretched
exponential tails in the presence of the cut-off introduced in \cite{Taka} is
explained theoretically. We end by briefly listing applications.Comment: Extended version (7 pages). Phys. Rev. E (to appear April 1998
Effective Hamiltonians in quantum optics: a systematic approach
We discuss a general and systematic method for obtaining effective
Hamiltonians that describe different nonlinear optical processes. The method
exploits the existence of a nonlinear deformation of the usual su(2) algebra
that arises as the dynamical symmetry of the original model. When some physical
parameter, dictated by the process under consideration, becomes small, we
immediately get a diagonal effective Hamiltonian that correctly represents the
dynamics for arbitrary states and long times. We extend the technique to su(3)
and su(N), finding the corresponding effective Hamiltonians when some resonance
conditions are fulfilled.Comment: 13 Pages, no figures, submitted for publicatio
Asymptotic power law of moments in a random multiplicative process with weak additive noise
It is well known that a random multiplicative process with weak additive
noise generates a power-law probability distribution. It has recently been
recognized that this process exhibits another type of power law: the moment of
the stochastic variable scales as a function of the additive noise strength. We
clarify the mechanism for this power-law behavior of moments by treating a
simple Langevin-type model both approximately and exactly, and argue this
mechanism is universal. We also discuss the relevance of our findings to noisy
on-off intermittency and to singular spatio-temporal chaos recently observed in
systems of non-locally coupled elements.Comment: 11 pages, 9 figures, submitted to Phys. Rev.
Polymer transport in random flow
The dynamics of polymers in a random smooth flow is investigated in the
framework of the Hookean dumbbell model. The analytical expression of the
time-dependent probability density function of polymer elongation is derived
explicitly for a Gaussian, rapidly changing flow. When polymers are in the
coiled state the pdf reaches a stationary state characterized by power-law
tails both for small and large arguments compared to the equilibrium length.
The characteristic relaxation time is computed as a function of the Weissenberg
number. In the stretched state the pdf is unstationary and exhibits
multiscaling. Numerical simulations for the two-dimensional Navier-Stokes flow
confirm the relevance of theoretical results obtained for the delta-correlated
model.Comment: 28 pages, 6 figure
Quantum jumps in hydrogen-like systems
In this paper it is shown that the Lyman- transition of a single
hydrogen-like system driven by a laser exhibits macroscopic dark periods,
provided there exists an additional constant electric field. We describe the
photon-counting process under the condition that the polarization of the laser
coincides with the direction of the constant electric field. The theoretical
results are given for the example of . We show that the emission
behavior depends sensitively on the Lamb shift (W.E. Lamb, R.C. Retherford,
Phys. Rev. 72, 241 (1947)) between the and energy levels.
A possibly realizable measurement of the mean duration of the dark periods
should give quantitative information about the above energy difference by using
the proposed photon-counting process.Comment: 7 pages RevTeX + 2 figures Phys. Rev A accepte
Master equations for effective Hamiltonians
We reelaborate on a general method for obtaining effective Hamiltonians that
describe different nonlinear optical processes. The method exploits the
existence of a nonlinear deformation of the su(2) algebra that arises as the
dynamical symmetry of the original model. When some physical parameter (usually
related to the dispersive limit) becomes small, we immediately get a diagonal
effective Hamiltonian that represents correctly the dynamics for arbitrary
states and long times. We apply the same technique to obtain how the noise
terms in the original model transform under this scheme, providing a systematic
way of including damping effects in processes described in terms of effective
Hamiltonians.Comment: 10 pages, no figure
Narrow Spectral Feature In Resonance Fluorescence With A Single Monochromatic Laser Field
We describe the resonance fluorescence spectrum of an atomic three-level
system where two of the states are coupled by a single monochromatic laser
field. The influence of the third energy level, which interacts with the two
laser-coupled states only via radiative decays, is studied in detail. For a
suitable choice of parameters, this system gives rise to a very narrow
structure at the laser frequency in the fluorescence spectrum which is not
present in the spectrum of a two-level atom. We find those parameter ranges by
a numerical analysis and use the results to derive analytical expressions for
the additional narrow peak. We also derive an exact expression for the peak
intensity under the assumption that a random telegraph model is applicable to
the system. This model and a simple spring model are then used to describe the
physical origins of the additional peak. Using these results, we explain the
connection between our system, a three-level system in V-configuration where
both transitions are laser driven, and a related experiment which was recently
reported.Comment: 14 pages, 15 figures, extension of the spring mode
The impact of the demographic transition on dengue in Thailand: Insights from a statistical analysis and mathematical modeling
Background: An increase in the average age of dengue hemorrhagic fever (DHF) cases has been reported in Thailand. The cause of this increase is not known. Possible explanations include a reduction in transmission due to declining mosquito populations, declining contact between human and mosquito, and changes in reporting. We propose that a demographic shift toward lower birth and death rates has reduced dengue transmission and lengthened the interval between large epidemics. Methods and Findings: Using data from each of the 72 provinces of Thailand, we looked for associations between force of infection (a measure of hazard, defined as the rate per capita at which susceptible individuals become infected) and demographic and climactic variables. We estimated the force of infection from the age distribution of cases from 1985 to 2005. We find that the force of infection has declined by 2% each year since a peak in the late 1970s and early 1980s. Contrary to recent findings suggesting that the incidence of DHF has increased in Thailand, we find a small but statistically significant decline in DHF incidence since 1985 in a majority of provinces. The strongest predictor of the change in force of infection and the mean force of infection is the median age of the population. Using mathematical simulations of dengue transmission we show that a reduced birth rate and a shift in the population's age structure can explain the shift in the age distribution of cases, reduction of the force of infection, and increase in the periodicity of multiannual oscillations of DHF incidence in the absence of other changes. Conclusions: Lower birth and death rates decrease the flow of susceptible individuals into the population and increase the longevity of immune individuals. The increase in the proportion of the population that is immune increases the likelihood that an infectious mosquito will feed on an immune individual, reducing the force of infection. Though the force of infection has decreased by half, we find that the critical vaccination fraction has not changed significantly, declining from an average of 85% to 80%. Clinical guidelines should consider the impact of continued increases in the age of dengue cases in Thailand. Countries in the region lagging behind Thailand in the demographic transition may experience the same increase as their population ages. The impact of demographic changes on the force of infection has been hypothesized for other diseases, but, to our knowledge, this is the first observation of this phenomenon
Conditional resonance-fluorescence spectra of single atoms.
Published versio
Resonance Fluorescence Spectrum of a Trapped Ion Undergoing Quantum Jumps
We experimentally investigate the resonance fluorescence spectrum of single
171Yb and 172Yb ions which are laser cooled to the Lamb-Dicke regime in a
radiofrequency trap. While the fluorescence scattering of 172Yb is continuous,
the 171Yb fluorescence is interrupted by quantum jumps because a nonvanishing
rate of spontaneous transitions leads to electron shelving in the metastable
hyperfine sublevel 2D3/2(F=2). The average duration of the resulting dark
periods can be varied by changing the intensity of a repumping laser field.
Optical heterodyne detection is employed to analyze the fluorescence spectrum
near the Rayleigh elastic scattering peak. It is found that the stochastic
modulation of the fluorescence emission by quantum jumps gives rise to a
Lorentzian component in the fluorescence spectrum, and that the linewidth of
this component varies according to the average duration of the dark
fluorescence periods. The experimental observations are in quantitative
agreement with theoretical predictions.Comment: 14 pages including 4 figures, pdf file, fig.1 replace
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