4,365 research outputs found
Finite-size effect and the components of multifractality in financial volatility
Many financial variables are found to exhibit multifractal nature, which is
usually attributed to the influence of temporal correlations and fat-tailedness
in the probability distribution (PDF). Based on the partition function approach
of multifractal analysis, we show that there is a marked finite-size effect in
the detection of multifractality, and the effective multifractality is the
apparent multifractality after removing the finite-size effect. We find that
the effective multifractality can be further decomposed into two components,
the PDF component and the nonlinearity component. Referring to the normal
distribution, we can determine the PDF component by comparing the effective
multifractality of the original time series and the surrogate data that have a
normal distribution and keep the same linear and nonlinear correlations as the
original data. We demonstrate our method by taking the daily volatility data of
Dow Jones Industrial Average from 26 May 1896 to 27 April 2007 as an example.
Extensive numerical experiments show that a time series exhibits effective
multifractality only if it possesses nonlinearity and the PDF has impact on the
effective multifractality only when the time series possesses nonlinearity. Our
method can also be applied to judge the presence of multifractality and
determine its components of multifractal time series in other complex systems.Comment: 9 RevTex pages including 9 eps figures. Comments and suggestions are
warmly welcom
Observation of many-body localization of interacting fermions in a quasi-random optical lattice
We experimentally observe many-body localization of interacting fermions in a
one-dimensional quasi-random optical lattice. We identify the many-body
localization transition through the relaxation dynamics of an
initially-prepared charge density wave. For sufficiently weak disorder the time
evolution appears ergodic and thermalizing, erasing all remnants of the initial
order. In contrast, above a critical disorder strength a significant portion of
the initial ordering persists, thereby serving as an effective order parameter
for localization. The stationary density wave order and the critical disorder
value show a distinctive dependence on the interaction strength, in agreement
with numerical simulations. We connect this dependence to the ubiquitous
logarithmic growth of entanglement entropy characterizing the generic many-body
localized phase.Comment: 6 pages, 6 figures + supplementary informatio
Density excitations of a harmonically trapped ideal gas
The dynamic structure factor of a harmonically trapped Bose gas has been
calculated well above the Bose-Einstein condensation temperature by treating
the gas cloud as a canonical ensemble of noninteracting classical particles.
The static structure factor is found to vanish as wavenumber squared in the
long-wavelength limit. We also incorporate a relaxation mechanism
phenomenologically by including a stochastic friction force to study the
dynamic structure factor. A significant temperature dependence of the
density-fluctuation spectra is found. The Debye-Waller factor has been
calculated for the trapped thermal cloud as function of wavenumber and of
particle number. A substantial difference is found between clouds of small and
large particle number
Ultrahigh Bandwidth Spin Noise Spectroscopy: Detection of Large g-Factor Fluctuations in Highly n-Doped GaAs
We advance all optical spin noise spectroscopy (SNS) in semiconductors to
detection bandwidths of several hundred gigahertz by employing an ingenious
scheme of pulse trains from ultrafast laser oscillators as an optical probe.
The ultrafast SNS technique avoids the need for optical pumping and enables
nearly perturbation free measurements of extremely short spin dephasing times.
We employ the technique to highly n-doped bulk GaAs where magnetic field
dependent measurements show unexpected large g-factor fluctuations.
Calculations suggest that such large g-factor fluctuations do not necessarily
result from extrinsic sample variations but are intrinsically present in every
doped semiconductor due to the stochastic nature of the dopant distribution.Comment: 5 pages, 3 figure
Thermodynamic time asymmetry in nonequilibrium fluctuations
We here present the complete analysis of experiments on driven Brownian
motion and electric noise in a circuit, showing that thermodynamic entropy
production can be related to the breaking of time-reversal symmetry in the
statistical description of these nonequilibrium systems. The symmetry breaking
can be expressed in terms of dynamical entropies per unit time, one for the
forward process and the other for the time-reversed process. These entropies
per unit time characterize dynamical randomness, i.e., temporal disorder, in
time series of the nonequilibrium fluctuations. Their difference gives the
well-known thermodynamic entropy production, which thus finds its origin in the
time asymmetry of dynamical randomness, alias temporal disorder, in systems
driven out of equilibrium.Comment: to be published in : Journal of Statistical Mechanics: theory and
experimen
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