Quantum signatures of classical multifractal measures

A clear signature of classical chaoticity in the quantum regime is the fractal Weyl law, which connects the density of eigenstates to the dimension $D_0$ of the classical invariant set of open systems. Quantum systems of interest are often {\it partially} open (e.g., cavities in which trajectories are partially reflected/absorbed). In the corresponding classical systems $D_0$ is trivial (equal to the phase-space dimension), and the fractality is manifested in the (multifractal) spectrum of R\'enyi dimensions $D_q$. In this paper we investigate the effect of such multifractality on the Weyl law. Our numerical simulations in area-preserving maps show for a wide range of configurations and system sizes $M$ that (i) the Weyl law is governed by a dimension different from $D_0=2$ and (ii) the observed dimension oscillates as a function of $M$ and other relevant parameters. We propose a classical model which considers an undersampled measure of the chaotic invariant set, explains our two observations, and predicts that the Weyl law is governed by a non-trivial dimension $D_\mathrm{asymptotic} < D_0$ in the semi-classical limit $M\rightarrow\infty$

A LEED determination of the structures of Ru(001) and of CO/Ru(001)−(√3 × √3)R30°

The structures of Ru(001) and of the √3 × √3 R30° overlayer of CO on Ru(001) have been determined by LEED I–V measurements and comparison to calculations. Special attention was paid to accurate angular alignment, selection of a well-ordered portion of the surface, and avoidance of beam-induced changes of the CO layer. Five orders of reflexes over a range of 300 eV each were used for the clean surface and 7 orders over 200 eV each for the CO superstructure. For the clean surface, a slight contraction of the first layer spacing (by 2%) was found which gave r-factors of 0.04 (Zanazzi-Jona) and 0.16 (Pendry) for 5 non-degenerate beams. For the CO structure the most probable geometry is the on-top site with spacings d(Ru---C) = 2.0 ± 0.1 Åandd(C---O) = 1.10 ± 0.1 Å (rZJ = 0.21; rP = 0.51). The two threefold hollow and the bridge sites can be clearly excluded

Cable Design for FAIR SIS 300

GSI, Darmstadt is preparing to build FAIR (Facility for Antiproton and Ion Research) which include SIS 300, a 300T - m fast-ramping heavy ion synchrotron. Dipoles for this ring will be 2.9 m long, producing 6 T over a 100 mm coil aperture and ramped at 1 T/s. The cable for these dipoles must have low losses and produce acceptable field distortions during the fast ramp. We plan to achieve this objective by using fine (~ 3 mum) filaments of NbTi in a wire with an interfilamentary matrix of CuMn to reduce proximity coupling and increase the transverse resistivity. The Rutherford cable have a thin stainless steel core and the wires will be coated with SnAg solder which has been oxidized, using a recipe similar to that developed at CERN, to increase the adjacent strand resistance Ra. Measurements of crossover strand resistance Re and Ra in cored cable with oxidized SnAg coating will be presented, together with data on critical current, persistent current magnetization and eddy current coupling in a wire with ultra fine filaments and a CuMn matrix in the interfilamentary region of the wire. These data will be used to predict losses and field distortion in the SIS 300 dipole and optimize the final design of cable for FAIR

Scanning Photo-Induced Impedance Microscopy - Resolution studies and polymer characterization

Scanning Photo-Induced Impedance Microscopy (SPIM) is an impedance imaging technique that is based on photocurrent measurements at field-effect structures. The material under investigation is deposited onto a semiconductor-insulator substrate. A thin metal film or an electrolyte solution with an immersed electrode serves as the gate contact. A modulated light beam focused into the space charge region of the semiconductor produces a photocurrent, which is directly related to the local impedance of the material. The absolute impedance of a polymer film can be measured by calibrating photocurrents using a known impedance in series with the sample. Depending on the wavelength of light used, charge carriers are not only generated in the focus but also throughout the bulk of the semiconductor. This can have adverse effects on the lateral resolution. Two-photon experiments were carried out to confine charge carrier generation to the spacecharge layer. The lateral resolution of SPIM is also limited by the lateral diffusion of charge carriers in the semiconductor. This problem can be solved by using thin silicon layers as semiconductor substrates. A resolution of better than 1 mu m was achieved using silicon on sapphire (SOS) substrates with a I l.Lm thick silicon layer

A LEED structural analysis of the Co(100) surface

The structure of the clean Co(1010) surface has been analysed by LEED. Application of a recently developed computational scheme reveals the prevalence of the termination A in which the two topmost layers exhibit a narrow spacing of 0.62 Å, corresponding to a 12.8(±0.5)% contraction with respect to the bulk value, while the spacing between the second and third layer is slightly expanded by 0.8(±0.2)%

Giant Kohn anomaly and the phase transition in charge density wave ZrTe_3

A strong Kohn anomaly in ZrTe_3 is identified in the mostly transverse acoustic phonon branch along the modulation vector q_P with polarization along the a* direction. This soft mode freezes to zero frequency at the transition temperature T_P and the temperature dependence of the frequency is strongly affected by fluctuation effects. Diffuse x-ray scattering of the incommensurate superstructure shows a power law scaling of the intensity and the correlation length that is compatible with an order parameter of dimension n = 2.Comment: 4 pages, 4 figures. accepted at Phys. Rev. Let

Impact of ambient oxygen on the surface structure of α-Cr2O3(0001)

Surface x-ray diffraction has been employed to quantitatively assess the surface structure of α-Cr2O3(0001) as a function of oxygen partial pressure at room temperature. In ultrahigh vacuum, the surface is found to exhibit a partially occupied double layer of chromium atoms. At an oxygen partial pressure of 1×10−2 mbar, the surface is determined to be terminated by chromyl species (CrO), clearly demonstrating that the presence of oxygen can significantly influence the structure of α-Cr2O3(0001)

A novel procedure for fast surface structural analysis based on LEED intensity data

By evaluating LEED intensities from different diffraction beams taken only at discrete energy intervals (which may be as large as 15–20 eV) the same degree of reliability in surface structure determination can be reached as with the conventional techniques based on analysis of continuous I/V-spectra. The minimum of the corresponding R-factor can be found by a least-squares fit method, as will be exemplified with a system in which 8 structural parameters were subject to simultaneous refinement

Planning stability in a product recorvery syste

Recovery of used products is an issue of growing importance due to customer expectations and environmental regulation. As a consequence, companies need to adapt their material management taking into account inbound flows of used products. Corresponding inventory control models have been proposed in literature. In this paper we address the issue of planning stability in a product recovery context. To this end, we consider rolling horizon planning for a stock point facing stochastic demand and product returns. We analyze the impact of the return flow on planning stability and compare the system behaviour with a traditional production environment. We show that structural results derived for traditional inventory models remain valid in a product recovery context. Moreover we discuss counterintuitive effects resulting from interaction between planning stability and stock levels. Zusammenfassung. In den letzten Jahren besteht aufgrund gesetzlicher Bestimmungen und gestiegenem Umweltbewußtsein in der Bevölkerung zunehmend die Tendenz, daßUnternehmen ihre Produkte nach deren Gebrauch vom Kunden zurücknehmen. Die Produktionsplanung und -steuerung der Unternehmen muß diesen Produktrückflüssen angepaßt werden. In der Literatur sind für verschiedene kreislaufwirtschaftliche Probleme optimale Lagerhaltungspolitiken abgeleitet worden. Dieser Beitrag beschäftigt sich mit der Planungsstabilität in einem kreislaufwirt- schaftlichen Basismodell, wo alle zurückkommenden Produkte aufgearbeitet werden müssen. Insbesondere wird der Einflußder Produktrückflüsse auf die Stabilität untersucht und ein Vergleich mit der Stabilität eines traditionellen Lagerhaltungsmodells durchgeführt. Es wird aufgezeigt, daß beide Modelle im wesentlichen dieselben strukturellen Eigenschaften besitzen