Localized and extended states in a disordered trap

We study Anderson localization in a disordered potential combined with an inhomogeneous trap. We show that the spectrum displays both localized and extended states, which coexist at intermediate energies. In the region of coexistence, we find that the extended states result from confinement by the trap and are weakly affected by the disorder. Conversely, the localized states correspond to eigenstates of the disordered potential, which are only affected by the trap via an inhomogeneous energy shift. These results are relevant to disordered quantum gases and we propose a realistic scheme to observe the coexistence of localized and extended states in these systems.Comment: Published versio

Emergence of complex and spinor wave functions in scale relativity. I. Nature of scale variables

One of the main results of Scale Relativity as regards the foundation of quantum mechanics is its explanation of the origin of the complex nature of the wave function. The Scale Relativity theory introduces an explicit dependence of physical quantities on scale variables, founding itself on the theorem according to which a continuous and non-differentiable space-time is fractal (i.e., scale-divergent). In the present paper, the nature of the scale variables and their relations to resolutions and differential elements are specified in the non-relativistic case (fractal space). We show that, owing to the scale-dependence which it induces, non-differentiability involves a fundamental two-valuedness of the mean derivatives. Since, in the scale relativity framework, the wave function is a manifestation of the velocity field of fractal space-time geodesics, the two-valuedness of velocities leads to write them in terms of complex numbers, and yields therefore the complex nature of the wave function, from which the usual expression of the Schr\"odinger equation can be derived.Comment: 36 pages, 5 figures, major changes from the first version, matches the published versio

Effectiveness of Implemented School Development Plan in Enhancing Quality Education in Public Secondary Schools in Ulanga District, Tanzania

The study examined the effectiveness of implemented School Development Planning (SDP) in enhancing quality education a case of public secondary schools in Ulanga District. Four research questions and one null hypothesis guided the study to elucidate the perception of heads of schools on the SDP. The study was guided by convergent parallel design under mixed research approach. The target population comprised of 17 public secondary schools and 17 heads of schools. Two secondary schools were used for pilot study. While the remaining 15 public secondary schools were all involved in the study. All the 15 heads of public secondary schools were involved in the study by virtue of their position and responsibility. Questionnaires and interview guide were administered to collect relevant data for the study. The study found out that not all the schools in Ulanga District had SDP. Also, the SDPs were not highly effective in enhancing quality education since some of the elements that enhance quality education were not implemented. The study further revealed that majority of the heads of schools had positive perception on the SDP as a tool toward improvement of teaching and learning in the schools; while a few of them had negative perception. The results from the tested null hypothesis reveals a moderate relationship between implementation of SDP and quality education. Thus, implementation of SDP to some extent enhances quality education which in turn improves students’ academic performance. The study concluded that the implemented SDP are moderately effective in enhancing various factors that ensure quality education in secondary schools. Furthermore, the study suggested that high cooperation should be emphasized between educational stakeholders in implementing SDPs for the improvement of quality of education in Ulanga District. The researcher suggested close follow up of the DEO, DQA and WEC on the development and implementation of SDP for effective improvement of teaching and learning

A Study of the Formation of Single- and Double-Walled Carbon Nanotubes by a CVD Method

The reduction in H2/CH4 atmosphere of aluminum-iron oxides produces metal particles small enough to catalyze the formation of single-walled carbon nanotubes. Several experiments have been made using the same temperature profile and changing only the maximum temperature (800-1070 °C). Characterizations of the catalyst materials are performed using notably 57Fe Mo¨ssbauer spectroscopy. Electron microscopy and a macroscopical method are used to characterize the nanotubes. The nature of the iron species (Fe3+, R-Fe, ç-Fe-C, Fe3C) is correlated to their location in the material. The nature of the particles responsible for the high-temperature formation of the nanotubes is probably an Fe-C alloy which is, however, found as Fe3C by postreaction analysis. Increasing the reduction temperature increases the reduction yield and thus favors the formation of surface-metal particles, thus producing more nanotubes. The obtained carbon nanotubes are mostly single-walled and double-walled with an average diameter close to 2.5 nm. Several formation mechanisms are thought to be active. In particular, it is shown that the second wall can grow inside the first one but that subsequent ones are formed outside. It is also possible that under given experimental conditions, the smallest (<2 nm) catalyst particles preferentially produce double-walled rather than single-walled carbon nanotubes

Experimental Investigation of Impact-Induced Molecular Desorption by 4.2 MeV/u Pb ions

In preparation for the heavy ion program of the LHC, accumulation and cooling test with lead ion beams have been performed in the LEAR storage ring. These tests have revealed that due to the unexpected, large outgassing of the vacuum system, the dynamic pressure of the ring could not be maintained low enough to reach the required beam intensities. To determine the actions necessary to lower the dynamic pressure rise, an experimental program has been initiated for measuring the molecular desorption yields of stainless steel vacuum chambers by the impact of 4.2 MeV/u lead ions with the charge states +27 and +53. The test chambers were exposed either at grazing or at perpendicular incidence. Different surface treatments are reported in terms of the molecular desorption yields for H2, CH4, CO and CO2. Unpexpected large values of molecular yields per incident ion up to 2x104 molecules/ion have been observed. The implications of these results for the vacuum system of the future ion accumulator ring (LEIR) and possible remedies to reduce the vacuum degradation will be discussed