Consideration of the relationship between Kepler and cyclotron dynamics leading to prediction of a non-MHD gravity-driven Hamiltonian dynamo

Conservation of canonical angular momentum shows that charged particles are typically constrained to stay within a poloidal Larmor radius of a poloidal magnetic flux surface. However, more detailed consideration shows that particles with a critical charge to mass ratio can have zero canonical angular momentum and so be both immune from centrifugal force and not constrained to stay in the vicinity of a specific flux surface. Suitably charged dust grains can have zero canonical angular momentum and in the presence of a gravitational field will spiral inwards across poloidal magnetic surfaces toward the central object and accumulate. This accumulation results in a gravitationally-driven dynamo, i.e., a mechanism for converting gravitational potential energy into a battery-like electric power source.Comment: 14 pages, 1 figur

Thermodynamical Properties of Hall Systems

We study quantum Hall effect within the framework of a newly proposed approach, which captures the principal results of some proposals. This can be established by considering a system of particles living on the non-commutative plane in the presence of an electromagnetic field and quantum statistical mechanically investigate its basic features. Solving the eigenvalue equation, we analytically derive the energy levels and the corresponding wavefunctions. These will be used, at low temperature and weak electric field, to determine the thermodynamical potential \Omega^{nc} and related physical quantities. Varying \Omega^{nc} with respect to the non-commutativity parameter \theta, we define a new function that can be interpreted as a \Omega^{nc} density. Evaluating the particle number, we show that the Hall conductivity of the system is \theta-dependent. This allows us to make contact with quantum Hall effect by offering different interpretations. We study the high temperature regime and discuss the magnetism of the system. We finally show that at \theta=2l_B^2, the system is sharing some common features with the Laughlin theory.Comment: 20 pages, misprints correcte

Coatings for FEL optics preparation and characterization of B4C and Pt

Large X ray mirrors are required for beam transport at both present day and future free electron lasers FELs and synchrotron sources worldwide. The demand for large mirrors with lengths up to 1 m single layers consisting of light or heavy elements has increased during the last few decades. Accordingly, surface finishing technology is now able to produce large substrate lengths with micro roughness on the sub nanometer scale. At the Helmholtz Zentrum Geesthacht HZG , a 4.5 m long sputtering facility enables us to deposit a desired single layer material some tens of nanometers thick. For the European XFEL project, the shape error should be less than 2 nm over the whole 1 m X ray mirror length to ensure the safe and efficient delivery of X ray beams to the scientific instruments. The challenge is to achieve thin film deposition on silicon substrates, benders and gratings without any change in mirror shape. Thin films of boron carbide and platinum with a thickness in the range 30 100 nm were manufactured using the HZG sputtering facility. This setup is able to cover areas of up to 1500 mm x120 mm in one step using rectangular sputtering sources. The coatings produced were characterized using various thin film methods. It was possible to improve the coating process to achieve a very high uniformity of the layer thickness. The movement of the substrate in front of the sputtering source has been optimized. Avariation in B4C layer thickness below 1 nm peak to valley was achieved at a mean thickness of 51.8 nm over a deposition length of 1.5 m. In the case of Pt, reflectometry and micro roughness measurements were performed. The uniformity in layer thickness was about 1 nm peak to valley . The micro roughness of the Pt layers showed no significant change in the coated state for layer thicknesses of 32 nm and 102 nm compared with the uncoated substrate state. The experimental results achieved will be discussed with regard to current restrictions and future development

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

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