7,662 research outputs found
Scaling laws for the photo-ionisation cross section of two-electron atoms
The cross sections for single-electron photo-ionisation in two-electron atoms
show fluctuations which decrease in amplitude when approaching the
double-ionisation threshold. Based on semiclassical closed orbit theory, we
show that the algebraic decay of the fluctuations can be characterised in terms
of a threshold law as with exponent
obtained as a combination of stability exponents of the triple-collision
singularity. It differs from Wannier's exponent dominating double ionisation
processes. The details of the fluctuations are linked to a set of infinitely
unstable classical orbits starting and ending in the non-regularisable triple
collision. The findings are compared with quantum calculations for a model
system, namely collinear helium.Comment: 4 pages, 1 figur
Record statistics for biased random walks, with an application to financial data
We consider the occurrence of record-breaking events in random walks with
asymmetric jump distributions. The statistics of records in symmetric random
walks was previously analyzed by Majumdar and Ziff and is well understood.
Unlike the case of symmetric jump distributions, in the asymmetric case the
statistics of records depends on the choice of the jump distribution. We
compute the record rate , defined as the probability for the th
value to be larger than all previous values, for a Gaussian jump distribution
with standard deviation that is shifted by a constant drift . For
small drift, in the sense of , the correction to
grows proportional to arctan and saturates at the value
. For large the record rate approaches a
constant, which is approximately given by
for .
These asymptotic results carry over to other continuous jump distributions with
finite variance. As an application, we compare our analytical results to the
record statistics of 366 daily stock prices from the Standard & Poors 500
index. The biased random walk accounts quantitatively for the increase in the
number of upper records due to the overall trend in the stock prices, and after
detrending the number of upper records is in good agreement with the symmetric
random walk. However the number of lower records in the detrended data is
significantly reduced by a mechanism that remains to be identified.Comment: 16 pages, 7 figure
Sivers effect in Drell Yan at RHIC
On the basis of a fit to the Sivers effect in deep-inelastic scattering, we
make predictions for single-spin asymmetries in the Drell-Yan process at RHIC.Comment: 10 pages, 7 figures, 1 table. v2: References and comments added,
minor correction
Record Statistics for Multiple Random Walks
We study the statistics of the number of records R_{n,N} for N identical and
independent symmetric discrete-time random walks of n steps in one dimension,
all starting at the origin at step 0. At each time step, each walker jumps by a
random length drawn independently from a symmetric and continuous distribution.
We consider two cases: (I) when the variance \sigma^2 of the jump distribution
is finite and (II) when \sigma^2 is divergent as in the case of L\'evy flights
with index 0 < \mu < 2. In both cases we find that the mean record number
grows universally as \sim \alpha_N \sqrt{n} for large n, but with a
very different behavior of the amplitude \alpha_N for N > 1 in the two cases.
We find that for large N, \alpha_N \approx 2 \sqrt{\log N} independently of
\sigma^2 in case I. In contrast, in case II, the amplitude approaches to an
N-independent constant for large N, \alpha_N \approx 4/\sqrt{\pi},
independently of 0<\mu<2. For finite \sigma^2 we argue, and this is confirmed
by our numerical simulations, that the full distribution of (R_{n,N}/\sqrt{n} -
2 \sqrt{\log N}) \sqrt{\log N} converges to a Gumbel law as n \to \infty and N
\to \infty. In case II, our numerical simulations indicate that the
distribution of R_{n,N}/\sqrt{n} converges, for n \to \infty and N \to \infty,
to a universal nontrivial distribution, independently of \mu. We discuss the
applications of our results to the study of the record statistics of 366 daily
stock prices from the Standard & Poors 500 index.Comment: 25 pages, 8 figure
Experimental Quantum Cryptography with Qutrits
We produce two identical keys using, for the first time, entangled trinary
quantum systems (qutrits) for quantum key distribution. The advantage of
qutrits over the normally used binary quantum systems is an increased coding
density and a higher security margin. The qutrits are encoded into the orbital
angular momentum of photons, namely Laguerre-Gaussian modes with azimuthal
index l +1, 0 and -1, respectively. The orbital angular momentum is controlled
with phase holograms. In an Ekert-type protocol the violation of a
three-dimensional Bell inequality verifies the security of the generated keys.
A key is obtained with a qutrit error rate of approximately 10 %.Comment: New version includes additional references and a few minor changes to
the manuscrip
Lieb-Robinson Bounds for Harmonic and Anharmonic Lattice Systems
We prove Lieb-Robinson bounds for the dynamics of systems with an infinite
dimensional Hilbert space and generated by unbounded Hamiltonians. In
particular, we consider quantum harmonic and certain anharmonic lattice
systems
Record statistics and persistence for a random walk with a drift
We study the statistics of records of a one-dimensional random walk of n
steps, starting from the origin, and in presence of a constant bias c. At each
time-step the walker makes a random jump of length \eta drawn from a continuous
distribution f(\eta) which is symmetric around a constant drift c. We focus in
particular on the case were f(\eta) is a symmetric stable law with a L\'evy
index 0 < \mu \leq 2. The record statistics depends crucially on the
persistence probability which, as we show here, exhibits different behaviors
depending on the sign of c and the value of the parameter \mu. Hence, in the
limit of a large number of steps n, the record statistics is sensitive to these
parameters (c and \mu) of the jump distribution. We compute the asymptotic mean
record number after n steps as well as its full distribution P(R,n). We
also compute the statistics of the ages of the longest and the shortest lasting
record. Our exact computations show the existence of five distinct regions in
the (c, 0 < \mu \leq 2) strip where these quantities display qualitatively
different behaviors. We also present numerical simulation results that verify
our analytical predictions.Comment: 51 pages, 22 figures. Published version (typos have been corrected
Pharmacokinetic profiles for oral and subcutaneous methotrexate in patients with Crohn\u27s disease
Background Methotrexate (MTX) is administered subcutaneously to Crohn\u27s Disease (CD) patients. There are very few studies evaluating the use of oral (PO) MTX in CD. A drug and its pharmaceutical alternative are equivalent (bioequivalence) when the bioavailability of the alternative falls within 80-125% of the bioavailability of the standard (US Food and Drug Administration - FDA). Aim To compare the pharmacokinetic (PK) profiles of PO and subcutaneous (SC) MTX in CD patients to determine the bioequivalence of these two routes. Methods Eleven patients received a PO and an SC MTX dose (25 mg) separated by one week over a two-week interval. Blood samples were collected at specified times over a 24-h period for each patient on two separate days. MTX plasma levels were obtained using sensitive mass spectrometry. Areas under the curve (AUC) were compared between the two routes. Results The mean AUC values were 3375 ng/mL × h (PO MTX) and 3985 ng/mL × h (SC MTX). The mean AUC ratio (PO/SC) was 0.86 (0.62-1.08). This correlates with a relative PO bioavailability of 86% in comparison to SC. The 90% confidence interval for the mean AUC (PO/SC) ratio is (0.785, 0.929). There were no adverse events. Conclusions The mean MTX AUC (PO/SC) in these patients falls outside the 90% confidence interval for the bioequivalence limit. SC MTX is more bioavailable than PO MTX; however, the mean relative MTX bioavailability (PO/SC) nearly met the FDA bioequivalence standard and PO MTX could be proposed in responders who would prefer this route. © 2012 Blackwell Publishing Ltd
Records and sequences of records from random variables with a linear trend
We consider records and sequences of records drawn from discrete time series
of the form , where the are independent and identically
distributed random variables and is a constant drift. For very small and
very large drift velocities, we investigate the asymptotic behavior of the
probability of a record occurring in the th step and the
probability that all entries are records, i.e. that . Our work is motivated by the analysis of temperature time series in
climatology, and by the study of mutational pathways in evolutionary biology.Comment: 21 pages, 7 figure
- …