Lattice oscillator model, scattering theory and a many-body problem

We propose a model for the quantum harmonic oscillator on a discrete lattice which can be written in supersymmetric form, in contrast with the more direct discretization of the harmonic oscillator. Its ground state is easily found to be annihilated by the annihilation operator defined here, and its excitation spectrum is obtained numerically. The versatility of the model is then used to calculate, in a simple way, the generalized position-dependent scattering length for a particle colliding with a single static impurity in a periodic potential and the exact ground state of an interacting many-body problem in a one-dimensional ring.Comment: 3 Figures. Version accepted in J. Phys.

Preparation and electrical characterization of the compound CuAgGeSe3

XIX Latin American Symposium on Solid State Physics (SLAFES XIX) IOP Publishing Journal of Physics: Conference Series 167 (2009)This work reports the synthesis and electrical characterization of the compound CuAgGeSe3. This material was synthesized by direct melting of the constituent elements, in their stoiochiometric ratio inside an evacuated quartz ampoule. The chemical analysis (EDX) confirmed the 1:1:1:3 stoichiometric ratios for the compound. The differential thermal analysis showed the existence of a principal phase that melts at 558ºC and a second phase at 636 ºC. The X-ray powder diffraction analysis indicated that the compound crystallizes in the monoclinic system, space group Cc, with unit cell parameters: a = 6.776(0) Å, b = 11.901(5) Å, c = 6.772(0) and β = 108.2(0)o. The study of the electrical properties was realized in the temperature range from 80 to 300 K and under a magnetic field of 14 kG. Employing the Mott transition model, we were able to obtain the temperature dependence of the resistivity and we estimated that the activation energy is 25.3 meV in the low temperatures region. The mobility temperature dependence is analyzed by taking into account the scattering of charge carriers by acoustic phonons, polar optic phonons and thermally activated hopping. From the analysis, the activation energy is estimated to be around 38 meV and the characteristic temperature of the phonons is estimated to be around 400 [email protected]@[email protected]@[email protected]