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

Electron pairing in periodic potentials under an external electric field

We study the semiclassical dynamics of interacting electrons in a biased crystal lattice. A complex dynamical scenario emerges from the interplay between the Coulomb and the external electric fields. When the electrons are far apart, the Coulomb potential may be small compared to the external potential and the electrons oscillate with effective Bloch frequencies, determined by the local electric field. In the opposite case, nearby electrons either separate or form a bound pair, depending on the initial energy compared to the band width. The pair due to the Coulomb field is stable even in the absence of the external field.Comment: 5 pages, 4 figures, some minor corrections and some additional reference

Cationic dyes immobilized on cellulose acetate surface modified with titanium dioxide: factorial design and an application as sensor for NADH

The electrochemical properties of meldola blue and toluidine blue cationic dyes immobilized on cellulose acetate surface modified with titanium dioxide were investigated by cyclic voltammetry. The materials synthesized were employed as carbon paste electrodes. The redox mediator properties of the meldola blue and toluidine blue chemically modified electrodes were optimized using a factorial design, consisting of two levels and four factors with two pseudo-central points (n= 20 experiments). The factorial analysis was carried out by searching for better reversibility of the redox process, such as the lowest separation between anodic and cathodic potential peaks and a current ratio near unity. The factors that presented significant effects on the overall optimization of the system to achieve the best conditions of the reversibility of electron transfer were the main factors scan rate and type of electrode (meldola blue or toluidine blue), besides the interaction factors KCl concentration × type of electrode (B×D) and the pH × [KCl] concentration × scan rate (A×B×C) interaction. The best electrochemical reversibility conditions obtained were: using the CA-TiO2-MB electrode, 1.0 mol L-1 KCl as supporting electrolyte, at scan rate of 10.0 mV s-1. Afterwards, the CA-TiO2-MB modified electrode was tested as an amperometric sensor for the determination of NADH, with a detection limit of 0.1 µmol L-1.As propriedades eletroquímicas dos corantes catiônicos, azul de meldola e azul de toluidina, imobilizados na superfície do acetato de celulose modificado com dióxido de titânio foram investigadas por voltametria cíclica. Os materiais sintetizados foram empregados como eletrodos de pasta de carbono. As propriedades mediadoras redox dos eletrodos modificados quimicamente com azul de meldola e azul de toluidina foram otimizadas utilizando um planejamento fatorial consistindo de dois níveis e quatro fatores com dois pseudo-pontos centrais (n=20 experimentos). A análise fatorial foi realizada para investigar as melhores condições de reversibilidade do processo redox tais como uma diminuição na separação entre os picos de potenciais anódico e catódico e razão de corrente próxima da unidade. Os fatores que apresentaram efeitos significantes na otimização global do sistema e que permitiram alcançar as melhores condições de reversibilidade de transferência de elétrons foram os fatores principais velocidade de varredura e tipo de eletrodo (azul de meldola ou azul de toluidina) além dos fatores de interação concentração do KCl × tipo de eletrodo (B×D) e a interação pH × [KCl] × velocidade de varredura (A×B×C). As melhores condições de reversibilidade eletroquímica obtidas foram: o eletrodo CA-TiO2-MB, KCl 1,0 mol L-1 como eletrólito suporte e velocidade de varredura de 10,0 mV s-1. Adicionalmente, o eletrodo modificado CA-TiO2-MB foi testado como sensor amperométrico para a determinação de NADH com um limite de detecção de 0,1 µmol L-1.14621472Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES

Magnon delocalization in ferromagnetic chains with long-range correlated disorder

We study one-magnon excitations in a random ferromagnetic Heisenberg chain with long-range correlations in the coupling constant distribution. By employing an exact diagonalization procedure, we compute the localization length of all one-magnon states within the band of allowed energies $E$. The random distribution of coupling constants was assumed to have a power spectrum decaying as $S(k)\propto 1/k^{\alpha}$. We found that for $\alpha < 1$, one-magnon excitations remain exponentially localized with the localization length $\xi$ diverging as 1/E. For $\alpha = 1$ a faster divergence of $\xi$ is obtained. For any $\alpha > 1$, a phase of delocalized magnons emerges at the bottom of the band. We characterize the scaling behavior of the localization length on all regimes and relate it with the scaling properties of the long-range correlated exchange coupling distribution.Comment: 7 Pages, 5 figures, to appear in Phys. Rev.

Non-Hermitian SUSY Hydrogen-like Hamiltonians with real spectra

It is shown that the radial part of the Hydrogen Hamiltonian factorizes as the product of two not mutually adjoint first order differential operators plus a complex constant epsilon. The 1-susy approach is used to construct non-hermitian Hamiltonians with hydrogen spectra. Other non-hermitian Hamiltonians are shown to admit an extra `complex energy' at epsilon. New self-adjoint hydrogen-like Hamiltonians are also derived by using a 2-susy transformation with complex conjugate pairs epsilon, (c.c) epsilon.Comment: LaTeX2e file, 13 pages, 6 EPS figures. New references added. The present is a reorganized and simplified versio