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Within the one-dimensional Hubbard model linear closed chains with various numbers of sites are considered in the self-consistent random phase approximation ͑SCRPA͒. Excellent results with a minimal numerical effort are obtained for ͑2+4n͒-site cases, confirming earlier results with this theory for other models. However, the 4n-site cases need further consideration. The SCRPA solves the two-site problem exactly. It therefore contains the two-electron and high-density Fermi gas limits correctly.

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β- In 2 S 3 and β-In2−xAlxS3 thin films have been deposited on different substrates using the spray pyrolysis technique at 320 °C. X-ray diffraction, atomic force microscopy, and scanning electron microscopy were used to characterize the structure of the films; the surface compositions of the films were studied by Auger electrons spectroscopy and energy dispersive spectrometry (EDS), the work function and the photovoltage by the Kelvin method. Using these techniques, we have specified the effect of the nature of the substrate, of its surface morphology, of the introduction of small amounts of Al in the layer, on the properties of the films. The best crystallized of β-In2S3 were obtained for deposits on pyrex. This was improved by the introduction of Al atoms. The work function differences (φmaterial–φprobe) for β-In2S3 and β-In2−xAlxS3 deposited on steel were equal to −150 meV and to −180 meV, respectively. Putting Al atoms in the film increases φm (by about 30 meV) and induces the formation of a negative surface barrier. The concentration of In, S, and O elements increased when the samples were annealed under a vacuum, whereas the concentration of carbon decreased. The best composition was obtained for In2S3 deposited on SnO2 and annealed. The introduction of Al increases O and C concentrations and reduce In, Cl, and S concentrations. Analysis of the film compositions by EDS gives the following concentrations [In]=37%, [S]=52%, and [Cl]=11%.

Self-consistent quasiparticle random phase approximation ͑SCQRPA͒ is for the first time applied to a more level pairing case. Various filling situations and values for the coupling constant are considered. Very encouraging results in comparison with the exact solution of the model are obtained. The nature of the low-lying mode in SCQRPA is identified. The strong reduction of the number fluctuation in SCQRPA vs BCS is pointed out. The transition from superfluidity to the normal fluid case is carefully investigated.