Adiabatic Evolution for Systems with Infinitely many Eigenvalue Crossings

We formulate an adiabatic theorem adapted to models that present an instantaneous eigenvalue experiencing an infinite number of crossings with the rest of the spectrum. We give an upper bound on the leading correction terms with respect to the adiabatic limit. The result requires only differentiability of the considered spectral projector, and some geometric hypothesis on the local behaviour of the eigenvalues at the crossings

General Adiabatic Evolution with a Gap Condition

We consider the adiabatic regime of two parameters evolution semigroups generated by linear operators that are analytic in time and satisfy the following gap condition for all times: the spectrum of the generator consists in finitely many isolated eigenvalues of finite algebraic multiplicity, away from the rest of the spectrum. The restriction of the generator to the spectral subspace corresponding to the distinguished eigenvalues is not assumed to be diagonalizable. The presence of eigenilpotents in the spectral decomposition of the generator forbids the evolution to follow the instantaneous eigenprojectors of the generator in the adiabatic limit. Making use of superadiabatic renormalization, we construct a different set of time-dependent projectors, close to the instantaneous eigeprojectors of the generator in the adiabatic limit, and an approximation of the evolution semigroup which intertwines exactly between the values of these projectors at the initial and final times. Hence, the evolution semigroup follows the constructed set of projectors in the adiabatic regime, modulo error terms we control

Smooth adiabatic evolutions with leaky power tails

Adiabatic evolutions with a gap condition have, under a range of circumstances, exponentially small tails that describe the leaking out of the spectral subspace. Adiabatic evolutions without a gap condition do not seem to have this feature in general. This is a known fact for eigenvalue crossing. We show that this is also the case for eigenvalues at the threshold of the continuous spectrum by considering the Friedrichs model.Comment: Final form, to appear in J. Phys. A; 11 pages, no figure

Capturing the Nature of the Spelling Errors in Developmental Language Disorder: A Scoping Review

Purpose: This scoping review aims to identify and analyze the nature of the spelling errors produced by children with developmental language disorder (DLD) across different orthographies. Building on a previous meta-analysis identifying the extent of the spelling difficulties of children with DLD, the review extends our understanding of the nature of the spelling errors produced by children with DLD. Three questions are addressed: Do spelling difficulties in children with DLD stem from weak phonological, orthographic, or morphological representations? What are the patterns of spelling performance in DLD depending on orthographic depth? Do comorbid difficulties with DLD impact spelling? / Method: The scoping review followed the five phases outlined by Arksey and O'Malley (2005) and extended by Levac et al. (2010): (a) specifying the research question; (b) identifying relevant studies; (c) selecting studies; (d) charting the data; and (e) collating, summarizing, and reporting the results. / Results: Eighteen studies that provided a qualitative description of the nature of spelling errors produced by children and adolescents with DLD were identified. Spelling performance was examined in relation to control groups that were matched on age, on language features (language, spelling, or reading age), or on co-occurring difficulties. / Conclusions: This review article highlights the key elements that need to be considered when practitioners examine spelling difficulties and provides benchmarks for assessment in a range of alphabetic languages for school-age children. The qualitative analyses indicated that when practitioners evaluate spelling performance in children or adolescents with DLD, three factors should be considered: phonological representations, morphological awareness, and reading skills

Correlated Markov Quantum Walks

We consider the discrete time unitary dynamics given by a quantum walk on $\Z^d$ performed by a particle with internal degree of freedom, called coin state, according to the following iterated rule: a unitary update of the coin state takes place, followed by a shift on the lattice, conditioned on the coin state of the particle. We study the large time behavior of the quantum mechanical probability distribution of the position observable in $\Z^d$ for random updates of the coin states of the following form. The random sequences of unitary updates are given by a site dependent function of a Markov chain in time, with the following properties: on each site, they share the same stationnary Markovian distribution and, for each fixed time, they form a deterministic periodic pattern on the lattice. We prove a Feynman-Kac formula to express the characteristic function of the averaged distribution over the randomness at time $n$ in terms of the nth power of an operator $M$. By analyzing the spectrum of $M$, we show that this distribution posesses a drift proportional to the time and its centered counterpart displays a diffusive behavior with a diffusion matrix we compute. Moderate and large deviations principles are also proven to hold for the averaged distribution and the limit of the suitably rescaled corresponding characteristic function is shown to satisfy a diffusion equation. An example of random updates for which the analysis of the distribution can be performed without averaging is worked out. The random distribution displays a deterministic drift proportional to time and its centered counterpart gives rise to a random diffusion matrix whose law we compute. We complete the picture by presenting an uncorrelated example.Comment: 37 pages. arXiv admin note: substantial text overlap with arXiv:1010.400

High-Throughput Qualitative and Quantitative Drug Checking by MALDI HRMS.

Illicit drugs are a global health problem, since both their acute and chronic consumption have negative impacts on the drug user's health. Drug checking facilities are receiving growing interest as they allow drug users to chemically analyze their product prior to consumption to assess the presence of adulterants or other non-expected substances. Such harm reduction programs allow the reduction of the risks associated with drug consumption without encouraging it. In particular, the emergence of new psychoactive substances (NPS) emphasizes the risk for the population increasing the diversity and the lability of illicit drugs on the market. Analytical developments are required to catch up with this rapid evolution and reduce the potential harm caused by such consumption. In this study, we developed a matrix-assisted laser desorption/ionization (MALDI) high-resolution mass spectrometry (HRMS) strategy for the high-throughput qualitative and quantitative analysis of drug checking samples. The use of online-based m/z cloud library for untargeted compound search improved the ability to identify unknown compounds. Sixty-seven drug checking samples were analyzed using this analytical strategy, allowing the detection of 10 designer drugs and several classical drugs of abuse (mainly cocaine and MDMA) as well as adulterants and contaminants. The results were then compared with routine analyses of the same samples using conventional approaches showing similar performance while removing the use of chromatographic separation thus resulting in a significant reduction of the time required for sample preparation and analysis. This study enlightens the potential of MALDI-HRMS as a high-throughput approach allowing to speed-up up to six times the identification and quantification of substances enabling to catch the fast changes on the drug of abuse market. This strategy could be an interesting alternative analytical approach, allowing better prevention and harm reduction for drug users

Spitzer observations of Bow Shocks and Outflows in RCW 38

We report Spitzer observations of five newly identified bow shocks in the massive star-forming region RCW 38. Four are visible at IRAC wavelengths, the fifth is visible only at 24 microns. Chandra X-ray emission indicates that winds from the central O5.5 binary, IRS~2, have caused an outflow to the NE and SW of the central subcluster. The southern lobe of hot ionised gas is detected in X-rays; shocked gas and heated dust from the shock-front are detected with Spitzer at 4.5 and 24 microns. The northern outflow may have initiated the present generation of star formation, based on the filamentary distribution of the protostars in the central subcluster. Further, the bow-shock driving star, YSO 129, is photo-evaporating a pillar of gas and dust. No point sources are identified within this pillar at near- to mid-IR wavelengths. We also report on IRAC 3.6 & 5.8 micron observations of the cluster DBS2003-124, NE of RCW 38, where 33 candidate YSOs are identified. One star associated with the cluster drives a parsec-scale jet. Two candidate HH objects associated with the jet are visible at IRAC and MIPS wavelengths. The jet extends over a distance of ~3 pc. Assuming a velocity of 100 km/s for the jet material gives an age of about 30,000 years, indicating that the star (and cluster) are likely to be very young, with a similar or possibly younger age than RCW 38, and that star formation is ongoing in the extended RCW 38 region.Comment: 27 pages, 6 figures, accepted to Ap

Random Time-Dependent Quantum Walks

We consider the discrete time unitary dynamics given by a quantum walk on the lattice $\Z^d$ performed by a quantum particle with internal degree of freedom, called coin state, according to the following iterated rule: a unitary update of the coin state takes place, followed by a shift on the lattice, conditioned on the coin state of the particle. We study the large time behavior of the quantum mechanical probability distribution of the position observable in $\Z^d$ when the sequence of unitary updates is given by an i.i.d. sequence of random matrices. When averaged over the randomness, this distribution is shown to display a drift proportional to the time and its centered counterpart is shown to display a diffusive behavior with a diffusion matrix we compute. A moderate deviation principle is also proven to hold for the averaged distribution and the limit of the suitably rescaled corresponding characteristic function is shown to satisfy a diffusion equation. A generalization to unitary updates distributed according to a Markov process is also provided. An example of i.i.d. random updates for which the analysis of the distribution can be performed without averaging is worked out. The distribution also displays a deterministic drift proportional to time and its centered counterpart gives rise to a random diffusion matrix whose law we compute. A large deviation principle is shown to hold for this example. We finally show that, in general, the expectation of the random diffusion matrix equals the diffusion matrix of the averaged distribution.Comment: Typos and minor errors corrected. To appear In Communications in Mathematical Physic

Arithmetic of split Kummer surfaces: Montgomery endomorphism of Edwards products

International audienceLet $E$ be an elliptic curve, $\mathcal{K}_1$ its Kummer curve $E/\{\pm1\}$, $E^2$ its square product, and $\mathcal{K}_2$ the split Kummer surface $E^2/\{\pm1\}$. The addition law on $E^2$ gives a large endomorphism ring, which induce endomorphisms of $\mathcal{K}_2$. With a view to the practical applications to scalar multiplication on $\mathcal{K}_1$, we study the explicit arithmetic of $\mathcal{K}_2$