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 $\sigma \propto |E|^{\mu}$ as $E \to 0_-$ with exponent $\mu$ 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 $P_n(c)$, defined as the probability for the $n$th value to be larger than all previous values, for a Gaussian jump distribution with standard deviation $\sigma$ that is shifted by a constant drift $c$. For small drift, in the sense of $c/\sigma \ll n^{-1/2}$, the correction to $P_n(c)$ grows proportional to arctan$(\sqrt{n})$ and saturates at the value $\frac{c}{\sqrt{2} \sigma}$. For large $n$ the record rate approaches a constant, which is approximately given by $1-(\sigma/\sqrt{2\pi}c)\textrm{exp}(-c^2/2\sigma^2)$ for $c/\sigma \gg 1$. 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 $X_{n}=Y_{n}+cn$, where the $Y_{n}$ are independent and identically distributed random variables and $c$ is a constant drift. For very small and very large drift velocities, we investigate the asymptotic behavior of the probability $p_n(c)$ of a record occurring in the $n$th step and the probability $P_N(c)$ that all $N$ entries are records, i.e. that $X_1 < X_2 < ... < X_N$. 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