Lifshitz Tails in Constant Magnetic Fields

We consider the 2D Landau Hamiltonian $H$ perturbed by a random alloy-type potential, and investigate the Lifshitz tails, i.e. the asymptotic behavior of the corresponding integrated density of states (IDS) near the edges in the spectrum of $H$. If a given edge coincides with a Landau level, we obtain different asymptotic formulae for power-like, exponential sub-Gaussian, and super-Gaussian decay of the one-site potential. If the edge is away from the Landau levels, we impose a rational-flux assumption on the magnetic field, consider compactly supported one-site potentials, and formulate a theorem which is analogous to a result obtained in the case of a vanishing magnetic field

Inverse Scattering for Gratings and Wave Guides

We consider the problem of unique identification of dielectric coefficients for gratings and sound speeds for wave guides from scattering data. We prove that the "propagating modes" given for all frequencies uniquely determine these coefficients. The gratings may contain conductors as well as dielectrics and the boundaries of the conductors are also determined by the propagating modes.Comment: 12 page

The XMM-Newton view of the Crab

Aims. We discuss the current X-ray view of the Crab Nebula and Pulsar, summarising our analysis of observations of the source with the EPIC-pn camera on board the XMM-Newton observatory. Different modes of EPIC-pn were combined in order to yield a complete scenario of the spectral properties of the Crab resolved in space and time (pulse phase). In addition we give a description of the special EPIC-pn Burst mode and guidance for data reduction in that mode. Methods. We analysed spectra for the nebula and pulsar separately in the 0.6−12.0 keV energy band. All data were processed with the SAS 6.0.0 XMM-Newton Scientific Analysis System package; models were fitted to the data with XSPEC 11. The high time resolution of EPIC-pn in its Burst mode (7 μs) was used for a phase resolved analysis of the pulsar spectrum, after determination of the period with epoch folding techniques. Data from the SmallWindow mode were processed and corrected for pile-up allowing for spectroscopy simultaneously resolved in space and time. Results. The spatial variation of the spectrum over the entire region of the Crab shows a gradual spectral softening from the inner pulsar region to the outer nebula region with a variation in photon index, Γ, from 2.0 to 2.4. Pulse phase resolved spectroscopy of the Crab Pulsar reveals a phase dependent modulation of the photon index in form of a significant hardening of the spectrum in the inter-peak phase from Γ = 1.7 during the pulse peak to Γ = 1.5

Studies of orbital parameters and pulse profile of the accreting millisecond pulsar XTE J1807-294

The accreting millisecond pulsar XTE J1807-294 was observed by XMM-Newton on March 22, 2003 after its discovery on February 21, 2003 by RXTE. The source was detected in its bright phase with an observed average count rate of 33.3 cts/s in the EPIC-pn camera in the 0.5-10 keV energy band (3.7 mCrab). Using the earlier established best-fit orbital period of 40.0741+/-0.0005 minutes from RXTE observations and considering a circular binary orbit as first approximation, we derived a value of 4.8+/-0.1 lt-ms for the projected orbital radius of the binary system and an epoch of the orbital phase of MJD 52720.67415(16). The barycentric mean spin period of the pulsar was derived as 5.2459427+/-0.0000004 ms. The pulsar's spin-pulse profile showed a prominent (1.5 ms FWHM) pulse, with energy and orbital phase dependence in the amplitude and shape. The measured pulsed fraction in four energy bands was found to be 3.1+/-0.2 % (0.5-3.0 keV), 5.4+/-0.4 % (3.0-6.0 keV), 5.1+/-0.7 % (6.0-10.0 keV) and 3.7+/-0.2 % (0.5-10.0 keV), respectively. Studies of spin-profiles with orbital phase and energy showed significant increase in its pulsed fraction during the second observed orbit of the neutron star, gradually declining in the subsequent two orbits, which was associated with sudden but marginal increase in mass accretion. From our investigations of orbital parameters and estimation of other properties of this compact binary system, we conclude that XTE J1807-294 is very likely a candidate for a millisecond radio pulsar.Comment: 4 pages, 4 figures, Accepted for publication in Astronomy and Astrophysics letter

Low lying spectrum of weak-disorder quantum waveguides

We study the low-lying spectrum of the Dirichlet Laplace operator on a randomly wiggled strip. More precisely, our results are formulated in terms of the eigenvalues of finite segment approximations of the infinite waveguide. Under appropriate weak-disorder assumptions we obtain deterministic and probabilistic bounds on the position of the lowest eigenvalue. A Combes-Thomas argument allows us to obtain so-called 'initial length scale decay estimates' at they are used in the proof of spectral localization using the multiscale analysis.Comment: Accepted for publication in Journal of Statistical Physics http://www.springerlink.com/content/0022-471

Gamma-widths, lifetimes and fluctuations in the nuclear quasi-continuum

Statistical $\gamma$-decay from highly excited states is determined by the nuclear level density (NLD) and the $\gamma$-ray strength function ($\gamma$SF). These average quantities have been measured for several nuclei using the Oslo method. For the first time, we exploit the NLD and $\gamma$SF to evaluate the $\gamma$-width in the energy region below the neutron binding energy, often called the quasi-continuum region. The lifetimes of states in the quasi-continuum are important benchmarks for a theoretical description of nuclear structure and dynamics at high temperature. The lifetimes may also have impact on reaction rates for the rapid neutron-capture process, now demonstrated to take place in neutron star mergers.Comment: CGS16, Shanghai 2017, Proceedings, 5 pages, 3 figure

Global Bounds for the Lyapunov Exponent and the Integrated Density of States of Random Schr\"odinger Operators in One Dimension

In this article we prove an upper bound for the Lyapunov exponent $\gamma(E)$ and a two-sided bound for the integrated density of states $N(E)$ at an arbitrary energy $E>0$ of random Schr\"odinger operators in one dimension. These Schr\"odinger operators are given by potentials of identical shape centered at every lattice site but with non-overlapping supports and with randomly varying coupling constants. Both types of bounds only involve scattering data for the single-site potential. They show in particular that both $\gamma(E)$ and $N(E)-\sqrt{E}/\pi$ decay at infinity at least like $1/\sqrt{E}$. As an example we consider the random Kronig-Penney model.Comment: 9 page

Localization Bounds for Multiparticle Systems

We consider the spectral and dynamical properties of quantum systems of $n$ particles on the lattice $\Z^d$, of arbitrary dimension, with a Hamiltonian which in addition to the kinetic term includes a random potential with iid values at the lattice sites and a finite-range interaction. Two basic parameters of the model are the strength of the disorder and the strength of the interparticle interaction. It is established here that for all $n$ there are regimes of high disorder, and/or weak enough interactions, for which the system exhibits spectral and dynamical localization. The localization is expressed through bounds on the transition amplitudes, which are uniform in time and decay exponentially in the Hausdorff distance in the configuration space. The results are derived through the analysis of fractional moments of the $n$-particle Green function, and related bounds on the eigenfunction correlators

Sharpness of the phase transition and exponential decay of the subcritical cluster size for percolation on quasi-transitive graphs

We study homogeneous, independent percolation on general quasi-transitive graphs. We prove that in the disorder regime where all clusters are finite almost surely, in fact the expectation of the cluster size is finite. This extends a well-known theorem by Menshikov and Aizenman & Barsky to all quasi-transitive graphs. Moreover we deduce that in this disorder regime the cluster size distribution decays exponentially, extending a result of Aizenman & Newman. Our results apply to both edge and site percolation, as well as long range (edge) percolation. The proof is based on a modification of the Aizenman & Barsky method.Comment: Latex 2e; 25 pages (a4wide); small editorial corrections; one reference adde

Novel inhibitors of human histone deacetylases: Design, synthesis and bioactivity of 3-alkenoylcoumarines

International audienceHistone deacetylases (HDACs) are well-established, promising targets for anticancer therapy due to their critical role in cancer development. Accordingly, an increasing number of HDAC inhibitors displaying cytotoxic effects against cancer cells have been reported. Among them, a large panel of chemical structures was described including coumarin-containing molecules. In this study, we described synthesis and biological activity of new coumarin-based derivatives as HDAC inhibitors. Among eight derivatives, three compounds showed HDAC inhibitory activities and antitumor activities against leukemia cell lines without affecting the viability of peripheral blood mononuclear cells from healthy donors