What is absolutely continuous spectrum?

This note is an expanded version of the author's contribution to the Proceedings of the ICMP Santiago, 2015, and is based on a talk given by the second author at the same Congress. It concerns a research program devoted to the characterization of the absolutely continuous spectrum of a self-adjoint operator H in terms of the transport properties of a suitable class of open quantum systems canonically associated to H

Femtosecond laser ablation of cemented carbides: properties and tribological applications

Laser ablation with fs laser pulses was performed in air on cobalt cemented tungsten carbide by means of a Ti : sapphire laser (800nm, 100fs). Small and moderate fluences (2, 5, 10J/cm2) and up to 5×104 pulses per irradiated spot were used to drill holes with aspect ratios up to 10. Cross-section cuts from laser-irradiated samples were produced and they were analysed with optical microscopy and SEM. EDX analyses were carried out on selected zones. Quasi-cylindrical holes were found for 2J/cm2, whereas for 5 and 10J/cm2 irregular shapes (lobes, bottoms wider than hole entrances) were found to occur after a given number of incident pulses. Layers with modified structure were evidenced at pore walls. SEM revealed a denser structure, while EDX analyses showed uniform and almost similar contents of W, C, and Co in these layers. As a direct application, patterning of coated WC-Co was carried out with 2J/cm2 and 100 pulses per pore. The resulted surfaces were tribologically tested and these tests revealed an improved friction and wear behaviou

Neuregulin/ErbB regulate neuromuscular junction development by phosphorylation of α-dystrobrevin

Neuregulin/ErbB signaling maintains high efficacy of synaptic transmission by stabilizing the postsynaptic apparatus via phosphorylation of α-dystrobrevin1

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

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

Zitterbewegung and semiclassical observables for the Dirac equation

In a semiclassical context we investigate the Zitterbewegung of relativistic particles with spin 1/2 moving in external fields. It is shown that the analogue of Zitterbewegung for general observables can be removed to arbitrary order in \hbar by projecting to dynamically almost invariant subspaces of the quantum mechanical Hilbert space which are associated with particles and anti-particles. This not only allows to identify observables with a semiclassical meaning, but also to recover combined classical dynamics for the translational and spin degrees of freedom. Finally, we discuss properties of eigenspinors of a Dirac-Hamiltonian when these are projected to the almost invariant subspaces, including the phenomenon of quantum ergodicity

Ion microscopy based on laser-cooled cesium atoms

We demonstrate a prototype of a Focused Ion Beam machine based on the ionization of a laser-cooled cesium beam and adapted for imaging and modifying different surfaces in the few-tens nanometer range. Efficient atomic ionization is obtained by laser promoting ground-state atoms into a target excited Rydberg state, then field-ionizing them in an electric field gradient. The method allows obtaining ion currents up to 130 pA. Comparison with the standard direct photo-ionization of the atomic beam shows, in our conditions, a 40-times larger ion yield. Preliminary imaging results at ion energies in the 1–5 keV range are obtained with a resolution around 40 nm, in the present version of the prototype. Our ion beam is expected to be extremely monochromatic, with an energy spread of the order of the eV, offering great prospects for lithography, imaging and surface analysis

Controlling plasma properties under differing degrees of electronegativity using odd harmonic dual frequency excitation

International audienceThe charged particle dynamics in low-pressure oxygen plasmas excited by odd harmonic dual frequency waveforms (low frequency of 13.56 MHz and high frequency of 40.68 MHz) are investigated using a one-dimensional numerical simulation in regimes of both low and high electronegativity. In the low electronegativity regime, the time and space averaged electron and negative ion densities are approximately equal and plasma sustainment is dominated by ionisation at the sheath expansion for all combinations of low and high frequency and the phase shift between them. In the high electronegativity regime, the negative ion density is a factor of 15--20 greater than the low electronegativity cases. In these cases, plasma sustainment is dominated by ionisation inside the bulk plasma and at the collapsing sheath edge when the contribution of the high frequency to the overall voltage waveform is low. As the high frequency component contribution to the waveform increases, sheath expansion ionisation begins to dominate. It is found that the control of the average voltage drop across the plasma sheath and the average ion flux to the powered electrode are similar in both regimes of electronegativity, despite the differing electron dynamics using the considered dual frequency approach. This offers potential for similar control of ion dynamics under a range of process conditions, independent of the electronegativity. This is in contrast to ion control offered by electrically asymmetric waveforms where the relationship between the ion flux and ion bombardment energy is dependent upon the electronegativity

Exogenous WNT5A and WNT11 proteins rescue CITED2 dysfunction in mouse embryonic stem cells and zebrafish morphants

Mutations and inadequate methylation profiles of CITED2 are associated with human congenital heart disease (CHD). In mouse, Cited2 is necessary for embryogenesis, particularly for heart development, and its depletion in embryonic stem cells (ESC) impairs cardiac differentiation. We have now determined that Cited2 depletion in ESC affects the expression of transcription factors and cardiopoietic genes involved in early mesoderm and cardiac specification. Interestingly, the supplementation of the secretome prepared from ESC overexpressing CITED2, during the onset of differentiation, rescued the cardiogenic defects of Cited2-depleted ESC. In addition, we demonstrate that the proteins WNT5A and WNT11 held the potential for rescue. We also validated the zebrafish as a model to investigate cited2 function during development. Indeed, the microinjection of morpholinos targeting cited2 transcripts caused developmental defects recapitulating those of mice knockout models, including the increased propensity for cardiac defects and severe death rate. Importantly, the co-injection of anti-cited2 morpholinos with either CITED2 or WNT5A and WNT11 recombinant proteins corrected the developmental defects of Cited2-morphants. This study argues that defects caused by the dysfunction of Cited2 at early stages of development, including heart anomalies, may be remediable by supplementation of exogenous molecules, offering the opportunity to develop novel therapeutic strategies aiming to prevent CHD.Agência financiadora: Fundação para a Ciência e a Tecnologia (FCT) Comissão de Coordenação e Desenvolvimento Regional do Algarve (CCDR Algarve) ALG-01-0145-FEDER-28044; DFG 568/17-2 Algarve Biomedical Center (ABC) Municipio de Louléinfo:eu-repo/semantics/publishedVersio