15,348 research outputs found
Extended Derivative Dispersion Relations
It is shown that, for a wide class of functions with physical interest as
forward scattering amplitudes, integral dispersion relations can be replaced by
derivative forms without any high-energy approximation. The applicability of
these extended derivative relations, in the investigation of forward
proton-proton and antiproton-proton elastic scattering, is exemplified by means
of a Pomeron-Reggeon model with totally nondegenerate trajectories.Comment: 7 pages, 1 figure, contribution to "Sense of Beauty in Physics",
Miniconference in Honor of Adriano Di Giacomo on his 70th Birthday, Pisa,
Italy, Jan. 26-27, 200
Derivative dispersion relations above the physical threshold
We discuss some formal and practical aspects related to the replacement of
Integral Dispersion Relations (IDR) by derivative forms, without high-energy
approximations. We first demonstrate that, for a class of functions with
physical interest as forward scattering amplitudes, this replacement can be
analytically performed, leading to novel Extended Derivative Dispersion
Relations (EDDR), which, in principle, are valid for any energy above the
physical threshold. We then verify the equivalence between the IDR and EDDR by
means of a popular parametrization for total cross sections from proton-proton
and antiproton-proton scattering and compare the results with those obtained
through other representations for the derivative relations. Critical aspects on
the limitations of the whole analysis, from both formal and practical points of
view, are also discussed in some detail.Comment: Final version, published in Brazilian Journal of Physics, V. 37, 358
(2007
Positive Lyapunov Exponents for Quasiperiodic Szego cocycles
In this paper we first obtain a formula of averaged Lyapunov exponents for
ergodic Szego cocycles via the Herman-Avila-Bochi formula. Then using
acceleration, we construct a class of analytic quasi-periodic Szego cocycles
with uniformly positive Lyapunov exponents. Finally, a simple application of
the main theorem in [Y] allows us to estimate the Lebesgue measure of support
of the measure associated to certain class of C1 quasiperiodic 2- sided
Verblunsky coefficients. Using the same method, we also recover the [S-S]
results for Schrodinger cocycles with nonconstant real analytic potentials and
obtain some nonuniform hyperbolicity results for arbitrarily fixed Brjuno
frequency and for certain C1 potentials.Comment: 27 papge
High-Energy Proton-Proton Forward Scattering and Derivative Analyticity Relations
We present the results of several parametrizations to two different ensemble
of data on total cross sections at the highest
center-of-mass energies (including cosmic-ray information). The results are
statistically consistent with two distinct scenarios at high energies. From one
ensemble the prediction for the LHC ( TeV) is mb and from the other, mb. From each
parametrization, and making use of derivative analyticity relations (DAR), we
determine (ratio between the forward real and imaginary parts of the
elastic scattering amplitude). A discussion on the optimization of the DAR in
terms of a free parameter is also presented.In all cases good descriptions of
the experimental data are obtained.Comment: One formula added, one unit changed, small misprints corrected, final
version to be published in Brazilian Journal of Physics; 13 pages, 8 figures,
aps-revte
Non-hermitian topology as a unifying framework for the Andreev versus Majorana states controversy
Zero-energy Andreev levels in hybrid semiconductor-superconductor nanowires mimic all expected Majorana phenomenology, including 2 e2∕ h conductance quantisation, even where band topology predicts trivial phases. This surprising fact has been used to challenge the interpretation of various transport experiments in terms of Majorana zero modes. Here we show that the Andreev versus Majorana controversy is clarified when framed in the language of non-Hermitian topology, the natural description for quantum systems open to the environment. This change of paradigm allows one to understand topological transitions and the emergence of zero modes in more general systems than can be described by band topology. This is achieved by studying exceptional point bifurcations in the complex spectrum of the system’s non-Hermitian Hamiltonian. Within this broader topological classification, Majoranas from both conventional band topology and a large subset of Andreev levels at zero energy are in fact topologically equivalent, which explains why they cannot be distinguishedWe thank J. Cayao for useful discussions in the early stages of this work. Research supported by the Spanish Ministry of Science, Innovation and Universities through Grants PGC2018-097018-B-I00, FIS2015-65706-P, FIS2015-64654-P, FIS2016-80434-P (AEI/FEDER, EU), the FPI programme BES-2016-078122, the Ramón y Cajal programme Grants RYC-2011-09345, RYC-2013-14645, the María de Maeztu Programme for Units of Excellence in R&D (MDM-2014-0377), and the European Union’s Horizon 2020 research and innovation programme under the FETOPEN Grant Agreement No. 828948. We also acknowledge support from CSIC Research Platform on Quantum Technologies PTI-00
Holder continuity of absolutely continuous spectral measures for one-frequency Schrodinger operators
We establish sharp results on the modulus of continuity of the distribution
of the spectral measure for one-frequency Schrodinger operators with
Diophantine frequencies in the region of absolutely continuous spectrum. More
precisely, we establish 1/2-Holder continuity near almost reducible energies
(an essential support of absolutely continuous spectrum). For
non-perturbatively small potentials (and for the almost Mathieu operator with
subcritical coupling), our results apply for all energies.Comment: 16 page
Optical Turbulence Measurements and Models for Mount John University Observatory
Site measurements were collected at Mount John University Observatory in 2005
and 2007 using a purpose-built scintillation detection and ranging system.
profiling indicates a weak layer located at 12 - 14 km above sea
level and strong low altitude turbulence extending up to 5 km. During calm
weather conditions, an additional layer was detected at 6 - 8 km above sea
level. profiling suggests that tropopause layer velocities are nominally
12 - 30 m/s, and near-ground velocities range between 2 -- 20 m/s, dependent on
weather. Little seasonal variation was detected in either and
profiles. The average coherence length, , was found to be cm for
the full profile at a wavelength of 589 nm. The average isoplanatic angle,
, was arcsec. The mean turbulence altitude,
, was found to be km above sea level. No average in the
Greenwood frequency, , could be established due to the gaps present in the
\vw\s profiles obtained. A modified Hufnagel-Valley model was developed to
describe the profiles at Mount John, which estimates at 6 cm
and at 0.9 arcsec. A series of models were developed, based
on the Greenwood wind model with an additional peak located at low altitudes.
Using the model and the suggested model for moderate ground
wind speeds, is estimated at 79 Hz.Comment: 14 pages; accepted for publication in PAS
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Numerical investigation of high-speed droplet impact using a multiscale two-fluid approach
A single droplet impact onto solid surfaces remains a fundamental and challenging topic in both experimental and numerical studies with significant importance in a plethora of industrial applications, ranging from printing technologies to fuel injection in internal combustion engines. Under high-speed impact conditions, additional complexities arise as a result of the prompt droplet splashing and the subsequent violent fragmentation; thus, different flow regimes and a vast spectrum of sizes for the produced secondary flow structures coexist in the flow field. The present work introduces a numerical methodology to capture the multiscale processes involved with respect to local topological characteristics. The proposed methodology concerns a compressible Σ-Υ two-fluid model with dynamic interface sharpening based on an advanced flow topology detection algorithm. The model has been developed in OpenFOAM® and provides the flexibility of dealing with the multiscale character of droplet splashing, by switching between a sharp and a diffuse interface within the Eulerian-Eulerian framework in segregated and dispersed flow regions, respectively. An additional transport equation for the interface surface area density (Σ) introduces important information for the sub-grid scale phenomena, which is exploited in the dispersed flow regions to provide an insight into the extended cloud of secondary droplets after impact on the target. A high-speed water droplet impact case has been examined and evaluated against new experimental data; these refer to a millimetre size droplet impacting a solid dry smooth surface at velocity as high as 150m/s, which corresponds to a Weber number of ~7.6×10^5. At the investigated impact conditions compressibility effects dominate the early stages of droplet splashing. A strong shock wave forms and propagates inside the droplet, where transonic Mach numbers occur; local Mach numbers up to 2.5 are observed for the expelled surrounding gas outside the droplet. The proposed numerical approach is found to capture relatively accurately the phenomena and provide significant information regarding the produced flow structure dimensions, which is not available from the experiment
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