Transmission resonances and supercritical states in a one dimensional cusp potential

We solve the two-component Dirac equation in the presence of a spatially one dimensional symmetric cusp potential. We compute the scattering and bound states solutions and we derive the conditions for transmission resonances as well as for supercriticality.Comment: 10 pages. Revtex 4. To appear in Phys Rev.

Finite temperature dynamics of vortices in the two dimensional anisotropic Heisenberg model

We study the effects of finite temperature on the dynamics of non-planar vortices in the classical, two-dimensional anisotropic Heisenberg model with XY- or easy-plane symmetry. To this end, we analyze a generalized Landau-Lifshitz equation including additive white noise and Gilbert damping. Using a collective variable theory with no adjustable parameters we derive an equation of motion for the vortices with stochastic forces which are shown to represent white noise with an effective diffusion constant linearly dependent on temperature. We solve these stochastic equations of motion by means of a Green's function formalism and obtain the mean vortex trajectory and its variance. We find a non-standard time dependence for the variance of the components perpendicular to the driving force. We compare the analytical results with Langevin dynamics simulations and find a good agreement up to temperatures of the order of 25% of the Kosterlitz-Thouless transition temperature. Finally, we discuss the reasons why our approach is not appropriate for higher temperatures as well as the discreteness effects observed in the numerical simulations.Comment: 12 pages, 8 figures, accepted for publication in European Physical Journal B (uses EPJ LaTeX

Dynamics and stability of Bose-Einstein solitons in tilted optical lattices

Bloch oscillations of Bose-Einstein condensates realize sensitive matter-wave interferometers. We investigate the dynamics and stability of bright-soliton wave packets in one-dimensional tilted optical lattices with a modulated mean-field interaction $g(t)$. By means of a time-reversal argument, we prove the stability of Bloch oscillations of breathing solitons that would be quasistatically unstable. Floquet theory shows that these breathing solitons can be more stable against certain experimental perturbations than rigid solitons or even non-interacting wave packets.Comment: final, published versio

Stability and decay of Bloch oscillations in presence of time-dependent nonlinearity

We consider Bloch oscillations of Bose-Einstein condensates in presence of a time-modulated s-wave scattering length. Generically, interaction leads to dephasing and decay of the wave packet. Based on a cyclic-time argument, we find---additionally to the linear Bloch oscillation and a rigid soliton solution---an infinite family of modulations that lead to a periodic time evolution of the wave packet. In order to quantitatively describe the dynamics of Bloch oscillations in presence of time-modulated interactions, we employ two complementary methods: collective-coordinates and the linear stability analysis of an extended wave packet. We provide instructive examples and address the question of robustness against external perturbations.Comment: 15 pages, 8 figures. Slightly amended final versio

Three-dimensional effects on extended states in disordered models of polymers

We study electronic transport properties of disordered polymers in the presence of both uncorrelated and short-range correlated impurities. In our procedure, the actual physical potential acting upon the electrons is replaced by a set of nonlocal separable potentials, leading to a Schr\"odinger equation that is exactly solvable in the momentum representation. We then show that the reflection coefficient of a pair of impurities placed at neighboring sites (dimer defect) vanishes for a particular resonant energy. When there is a finite number of such defects randomly distributed over the whole lattice, we find that the transmission coefficient is almost unity for states close to the resonant energy, and that those states present a very large localization length. Multifractal analysis techniques applied to very long systems demonstrate that these states are truly extended in the thermodynamic limit. These results reinforce the possibility to verify experimentally theoretical predictions about absence of localization in quasi-one-dimensional disordered systems.Comment: 16 pages, REVTeX 3.0, 5 figures on request from FDA ([email protected]). Submitted to Phys. Rev. B. MA/UC3M/09/9

Photonic realization of the relativistic Kronig-Penney model and relativistic Tamm surface states

Photonic analogues of the relativistic Kronig-Penney model and of relativistic surface Tamm states are proposed for light propagation in fibre Bragg gratings (FBGs) with phase defects. A periodic sequence of phase slips in the FBG realizes the relativistic Kronig-Penney model, the band structure of which being mapped into the spectral response of the FBG. For the semi-infinite FBG Tamm surface states can appear and can be visualized as narrow resonance peaks in the transmission spectrum of the grating

Exciton Optical Absorption in Self-Similar Aperiodic Lattices

Exciton optical absorption in self-similar aperiodic one-dimensional systems is considered, focusing our attention on Thue-Morse and Fibonacci lattices as canonical examples. The absorption line shape is evaluated by solving the microscopic equations of motion of the Frenkel-exciton problem on the lattice, in which on-site energies take on two values, according to the Thue-Morse or Fibonacci sequences. Results are compared to those obtained in random lattices with the same stechiometry and size. We find that aperiodic order causes the occurrence of well-defined characteristic features in the absorption spectra which clearly differ from the case of random systems, indicating a most peculiar exciton dynamics. We successfully explain the obtained spectra in terms of the two-center problem. This allows us to establish the origin of all the absorption lines by considering the self-similar aperiodic lattices as composed of two-center blocks, within the same spirit of the renormalization group ideas.Comment: 16 pages in REVTeX 3.0. 2 figures on request to F. D-A ([email protected]

Spatial distribution of vacancy defects in GaP wafers

Cathodoluminescencescanning electron microscopy and positron annihilation techniques have been used to investigate the distribution of defects in GaP wafers. The results show the existence of a gradient of the concentration of vacancy‐type defects along the wafer diameter, which causes inhomogeneity in the emission. Dislocation density and vacancy concentration profiles have been compared

Delocalization of states in two component superlattices with correlated disorder

Electron and phonon states in two different models of intentionally disordered superlattices are studied analytically as well as numerically. The localization length is calculated exactly and we found that it diverges for particular energies or frequencies, suggesting the existence of delocalized states for both electrons and phonons. Numerical calculations for the transmission coefficient support the existence of these delocalized states.Comment: RevTeX, 12 pages, 2 PS figures adde

Electron dynamics in intentionally disordered semiconductor superlattices

We study the dynamical behavior of disordered quantum-well-based semiconductor superlattices where the disorder is intentional and short-range correlated. We show that, whereas the transmission time of a particle grows exponentially with the number of wells in an usual disordered superlattice for any value of the incident particle energy, for specific values of the incident energy this time increases linearly when correlated disorder is included. As expected, those values of the energy coincide with a narrow subband of extended states predicted by the static calculations of Dom\'{\i}nguez-Adame {\em et al.} [Phys. Rev. B {\bf 51}, 14 ,359 (1994)]; such states are seen in our dynamical results to exhibit a ballistic regime, very close to the WKB approximation of a perfect superlattice. Fourier transform of the output signal for an incident Gaussian wave packet reveals a dramatic filtering of the original signal, which makes us confident that devices based on this property may be designed and used for nanotechnological applications. This is more so in view of the possibility of controllingthe outp ut band using a dc electric field, which we also discuss. In the conclusion we summarize our results and present an outlook for future developments arising from this work.Comment: 10 pagex, RevTex, 13 Postscript figures. Physical Review B (in press