1,929 research outputs found
Noise-free high-efficiency photon-number-resolving detectors
High-efficiency optical detectors that can determine the number of photons in
a pulse of monochromatic light have applications in a variety of physics
studies, including post-selection-based entanglement protocols for linear
optics quantum computing and experiments that simultaneously close the
detection and communication loopholes of Bell's inequalities. Here we report on
our demonstration of fiber-coupled, noise-free, photon-number-resolving
transition-edge sensors with 88% efficiency at 1550 nm. The efficiency of these
sensors could be made even higher at any wavelength in the visible and
near-infrared spectrum without resulting in a higher dark-count rate or
degraded photon-number resolution.Comment: 4 pages, 4 figures Published in Physical Review A, Rapid
Communications, 17 June 200
Fractional derivatives of random walks: Time series with long-time memory
We review statistical properties of models generated by the application of a
(positive and negative order) fractional derivative operator to a standard
random walk and show that the resulting stochastic walks display
slowly-decaying autocorrelation functions. The relation between these
correlated walks and the well-known fractionally integrated autoregressive
(FIGARCH) models, commonly used in econometric studies, is discussed. The
application of correlated random walks to simulate empirical financial times
series is considered and compared with the predictions from FIGARCH and the
simpler FIARCH processes. A comparison with empirical data is performed.Comment: 10 pages, 14 figure
Dynamics of Fractal Solids
We describe the fractal solid by a special continuous medium model. We
propose to describe the fractal solid by a fractional continuous model, where
all characteristics and fields are defined everywhere in the volume but they
follow some generalized equations which are derived by using integrals of
fractional order. The order of fractional integral can be equal to the fractal
mass dimension of the solid. Fractional integrals are considered as an
approximation of integrals on fractals. We suggest the approach to compute the
moments of inertia for fractal solids. The dynamics of fractal solids are
described by the usual Euler's equations. The possible experimental test of the
continuous medium model for fractal solids is considered.Comment: 12 pages, LaTe
Non-Markovian Levy diffusion in nonhomogeneous media
We study the diffusion equation with a position-dependent, power-law
diffusion coefficient. The equation possesses the Riesz-Weyl fractional
operator and includes a memory kernel. It is solved in the diffusion limit of
small wave numbers. Two kernels are considered in detail: the exponential
kernel, for which the problem resolves itself to the telegrapher's equation,
and the power-law one. The resulting distributions have the form of the L\'evy
process for any kernel. The renormalized fractional moment is introduced to
compare different cases with respect to the diffusion properties of the system.Comment: 7 pages, 2 figure
Stationarity-conservation laws for certain linear fractional differential equations
The Leibniz rule for fractional Riemann-Liouville derivative is studied in
algebra of functions defined by Laplace convolution. This algebra and the
derived Leibniz rule are used in construction of explicit form of
stationary-conserved currents for linear fractional differential equations. The
examples of the fractional diffusion in 1+1 and the fractional diffusion in d+1
dimensions are discussed in detail. The results are generalized to the mixed
fractional-differential and mixed sequential fractional-differential systems
for which the stationarity-conservation laws are obtained. The derived currents
are used in construction of stationary nonlocal charges.Comment: 28 page
State transition of a non-Ohmic damping system in a corrugated plane
Anomalous transport of a particle subjected to non-Ohmic damping of the power
in a tilted periodic potential is investigated via Monte Carlo
simulation of generalized Langevin equation. It is found that the system
exhibits two relative motion modes: the locking state and the running state.
Under the surrounding of sub-Ohmic damping (), the particle should
transfer into a running state from a locking state only when local minima of
the potential vanish; hence the particle occurs a synchronization oscillation
in its mean displacement and mean square displacement (MSD). In particular, the
two motion modes are allowed to coexist in the case of super-Ohmic damping
() for moderate driving forces, namely, where exists double centers
in the velocity distribution. This induces the particle having faster
diffusion, i.e., its MSD reads . Our result shows that the effective power index
can be enhanced and is a nonmonotonic function of the
temperature and the driving force. The mixture effect of the two motion modes
also leads to a breakdown of hysteresis loop of the mobility.Comment: 7 pages,7 figure
The W51 Giant Molecular Cloud
We present 45"-47" angular resolution maps at 50" sampling of the 12CO and
13CO J=1-0 emission toward a 1.39 deg x 1.33 deg region in the W51 HII region
complex. These data permit the spatial and kinematic separation of several
spectral features observed along the line of sight to W51, and establish the
presence of a massive (1.2 x 10^6 Mo), large (83 pc x 114 pc) giant molecular
cloud (GMC), defined as the W51 GMC, centered at (l,b,V) = (49.5 deg, -0.2 deg,
61 km/s). A second massive (1.9 x 10^5 Mo), elongated (136 pc x 22 pc)
molecular cloud is found at velocities of about 68 km/s along the southern edge
of the W51 GMC. Of the five radio continuum sources that classically define the
W51 region, the brightest source at lambda 6cm (G49.5-0.4) is spatially and
kinematically coincident with the W51 GMC and three (G48.9-0.3, G49.1-0.4, and
G49.2-0.4) are associated with the 68 km/s cloud. Published absorption line
spectra indicate that the fifth prominent continuum source (G49.4-0.3) is
located behind the W51 molecular cloud. The W51 GMC is among the upper 1% of
clouds in the Galactic disk by size and the upper 5-10% by mass. While the W51
GMC is larger and more massive than any nearby molecular cloud, the average H2
column density is not unusual given its size and the mean H2 volume density is
comparable to that in nearby clouds. The W51 GMC is also similar to other
clouds in that most of the molecular mass is contained in a diffuse envelope
that is not currently forming massive stars. We speculate that much of the
massive star formation activity in this region has resulted from a collision
between the 68 km/s cloud and the W51 GMC.Comment: Accepted for publication by the Astronomical Journal. 21 pages, plus
7 figures and 1 tabl
Levi-Civita cylinders with fractional angular deficit
The angular deficit factor in the Levi-Civita vacuum metric has been
parametrized using a Riemann-Liouville fractional integral. This introduces a
new parameter into the general relativistic cylinder description, the
fractional index {\alpha}. When the fractional index is continued into the
negative {\alpha} region, new behavior is found in the Gott-Hiscock cylinder
and in an Israel shell.Comment: 5 figure
Hyperbolic subdiffusive impedance
We use the hyperbolic subdiffusion equation with fractional time derivatives
(the generalized Cattaneo equation) to study the transport process of
electrolytes in media where subdiffusion occurs. In this model the flux is
delayed in a non-zero time with respect to the concentration gradient. In
particular, we obtain the formula of electrochemical subdiffusive impedance of
a spatially limited sample in the limit of large and of small pulsation of the
electric field. The boundary condition at the external wall of the sample are
taken in the general form as a linear combination of subdiffusive flux and
concentration of the transported particles. We also discuss the influence of
the equation parameters (the subdiffusion parameter and the delay time) on the
Nyquist impedance plots.Comment: 10 pages, 5 figure
Infrared spectroscopy of diatomic molecules - a fractional calculus approach
The eigenvalue spectrum of the fractional quantum harmonic oscillator is
calculated numerically solving the fractional Schr\"odinger equation based on
the Riemann and Caputo definition of a fractional derivative. The fractional
approach allows a smooth transition between vibrational and rotational type
spectra, which is shown to be an appropriate tool to analyze IR spectra of
diatomic molecules.Comment: revised + extended version, 9 pages, 6 figure
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