Growth of nano dots on the grazing incidence mirror surface under FEL irradiation Analytic approach to modeling

Simple analytic equation is deduced to explain new physical phenomenon detected experimentally growth of nano dots 40 55 nm diameter, 8 13 nm height, 9.4 dots amp; 956;m2 surface density on the grazing incidence mirror surface under the three years irradiation by the free electron laser FLASH 5 45 nm wavelength, 3 degrees grazing incidence angle . The growth model is based on the assumption that the growth of nano dots is caused by polymerization of incoming hydrocarbon molecules under the action of incident photons directly or photoelectrons knocked out from a mirror surface. The key feature of our approach consists in that we take into account the radiation intensity variation nearby a mirror surface in an explicit form, because the polymerization probability is proportional to it. We demonstrate that the simple analytic approach allows to explain all phenomena observed in experiment and to predict new effects. In particular, we show that the nano dots growth depends crucially on the grazing angle of incoming beam and its intensity growth of nano dots is observed in the limited from above and below intervals of the grazing angle and the radiation intensity. Decrease in the grazing angle by 1 degree only from 3 to 2 degree may result in a strong suppression of nanodots growth and their total disappearing. Similarly, decrease in the radiation intensity by several times replacement of free electron laser by synchrotron results also in disappearing of nano dots growt

Barycentric decomposition of quantum measurements in finite dimensions

We analyze the convex structure of the set of positive operator valued measures (POVMs) representing quantum measurements on a given finite dimensional quantum system, with outcomes in a given locally compact Hausdorff space. The extreme points of the convex set are operator valued measures concentrated on a finite set of k \le d^2 points of the outcome space, d< \infty being the dimension of the Hilbert space. We prove that for second countable outcome spaces any POVM admits a Choquet representation as the barycenter of the set of extreme points with respect to a suitable probability measure. In the general case, Krein-Milman theorem is invoked to represent POVMs as barycenters of a certain set of POVMs concentrated on k \le d^2 points of the outcome space.Comment: !5 pages, no figure

Upper bounds on the density of states of single Landau levels broadened by Gaussian random potentials

We study a non-relativistic charged particle on the Euclidean plane R^2 subject to a perpendicular constant magnetic field and an R^2-homogeneous random potential in the approximation that the corresponding random Landau Hamiltonian on the Hilbert space L^2(R^2) is restricted to the eigenspace of a single but arbitrary Landau level. For a wide class of Gaussian random potentials we rigorously prove that the associated restricted integrated density of states is absolutely continuous with respect to the Lebesgue measure. We construct explicit upper bounds on the resulting derivative, the restricted density of states. As a consequence, any given energy is seen to be almost surely not an eigenvalue of the restricted random Landau Hamiltonian.Comment: 16 pages, to appear in "Journal of Mathematical Physics

Variation of elastic scattering across a quantum well

The Drude scattering times of electrons in two subbands of a parabolic quantum well have been studied at constant electron sheet density and different positions of the electron distribution along the growth direction. The scattering times obtained by magnetotransport measurements decrease as the electrons are displaced towards the well edges, although the lowest-subband density increases. By comparing the measurements with calculations of the scattering times of a two-subband system, new information on the location of the relevant scatterers and the anisotropy of intersubband scattering is obtained. It is found that the scattering time of electrons in the lower subband depends sensitively on the position of the scatterers, which also explains the measured dependence of the scattering on the carrier density. The measurements indicate segregation of scatterers from the substrate side towards the quantum well during growth.Comment: 4 pages, 4 figure

Test for entanglement using physically observable witness operators and positive maps

Motivated by the Peres-Horodecki criterion and the realignment criterion we develop a more powerful method to identify entangled states for any bipartite system through a universal construction of the witness operator. The method also gives a new family of positive but non-completely positive maps of arbitrary high dimensions which provide a much better test than the witness operators themselves. Moreover, we find there are two types of positive maps that can detect 2xN and 4xN bound entangled states. Since entanglement witnesses are physical observables and may be measured locally our construction could be of great significance for future experiments.Comment: 6 pages, 1 figure, revtex4 styl

Flux of Atmospheric Neutrinos

Atmospheric neutrinos produced by cosmic-ray interactions in the atmosphere are of interest for several reasons. As a beam for studies of neutrino oscillations they cover a range of parameter space hitherto unexplored by accelerator neutrino beams. The atmospheric neutrinos also constitute an important background and calibration beam for neutrino astronomy and for the search for proton decay and other rare processes. Here we review the literature on calculations of atmospheric neutrinos over the full range of energy, but with particular attention to the aspects important for neutrino oscillations. Our goal is to assess how well the properties of atmospheric neutrinos are known at present.Comment: 68 pages, 26 figures. With permission from the Annual Review of Nuclear & Particle Science. Final version of this material is scheduled to appear in the Annual Review of Nuclear & Particle Science Vol. 52, to be published in December 2002 by Annual Reviews (http://annualreviews.org

Theory of Incompressible States in a Narrow Channel

We report on the properties of a system of interacting electrons in a narrow channel in the quantum Hall effect regime. It is shown that an increase in the strength of the Coulomb interaction causes abrupt changes in the width of the charge-density profile of translationally invariant states. We derive a phase diagram which includes many of the stable odd-denominator states as well as a novel fractional quantum Hall state at lowest half-filled Landau level. The collective mode evaluated at the half-filled case is strikingly similar to that for an odd-denominator fractional quantum Hall state.Comment: 4 pages, REVTEX, and 4 .ps file