Parametric oscillator in a Kerr medium: evolution of coherent states

We study the temporal evolution of a coherent state under the action of a parametric oscillator and a nonlinear Kerr-like medium. We make use of the interaction picture representation and use an exact time evolution operator for the time independent part of the Hamiltonian. We approximate the interaction picture Hamiltonian in such a way as to make it a member of a Lie algebra. The corresponding time evolution operator behaves like a squeezing operator due to the temporal dependence of the oscillator's frequency. We analyze the probability amplitude and the auto correlation function for different Hamiltonian parameters and we find a very good agreement between our approximate results and converged numerical calculations.Comment: 11 pages, 3 figure

Dynamics of the Formation of Bright Solitary Waves of Bose-Einstein Condensates in Optical Lattices

We present a detailed description of the formation of bright solitary waves in optical lattices. To this end, we have considered a ring lattice geometry with large radius. In this case, the ring shape does not have a relevant effect in the local dynamics of the condensate, while offering a realistic set up to implement experiments with conditions usually not available with linear lattices (in particular, to study collisions). Our numerical results suggest that the condensate radiation is the relevant dissipative process in the relaxation towards a self-trapped solution. We show that the source of dissipation can be attributed to the presence of higher order dispersion terms in the effective mass approach. In addition, we demonstrate that the stability of the solitary solutions is linked with particular values of the width of the wavepacket in the reciprocal space. Our study suggests that these critical widths for stability depend on the geometry of the energy band, but are independent of the condensate parameters (momentum, atom number, etc.). Finally, the non-solitonic nature of the solitary waves is evidenced showing their instability under collisions.Comment: 7 pages, 7 figures, to appear in PR

The mid-infrared extinction law in the darkest cores of the Pipe Nebula

Context. The properties of dust grains, in particular their size distribution, are expected to differ from the interstellar medium to the high-density regions within molecular clouds. Aims. We measure the mid-infrared extinction law produced by dense material in molecular cloud cores. Since the extinction at these wavelengths is caused by dust, the extinction law in cores should depart from that found in low-density environments if the dust grains have different properties. Methods. We use the unbiased LINES method to measure the slope of the reddening vectors in color-color diagrams. We derive the mid-infrared extinction law toward the dense cores B59 and FeSt 1-457 in the Pipe Nebula over a range of visual extinction between 10 and 50 magnitudes, using a combination of Spitzer/IRAC, and ESO NTT/VLT data. Results. The mid-infrared extinction law in both cores departs significantly from a power-law between 3.6 and 8 micron, suggesting that these cores contain dust with a considerable fraction of large dust grains. We find no evidence for a dependence of the extinction law with column density up to 50 magnitudes of visual extinction in these cores, and no evidence for a variation between our result and those for other clouds at lower column densities reported elsewhere in the literature. This suggests that either large grains are present even in low column density regions, or that the existing dust models need to be revised at mid-infrared wavelengths. We find a small but significant difference in the extinction law of the two cores, that we tentatively associate with the onset of star formation in B59.Comment: 8 pages, 6 figures. Accepted to A&

Enhancement of entanglement in one-dimensional disordered systems

The pairwise quantum entanglement of sites in disordered electronic one-dimensional systems (rings) is studied. We focus on the effect of diagonal and off diagonal disorder on the concurrence $C_{ij}$ between electrons on neighbor and non neighbor sites $i,j$ as a function of band filling. In the case of diagonal disorder, increasing the degree of disorder leads to a decrease of the concurrence with respect to the ordered case. However, off-diagonal disorder produces a surprisingly strong enhancement of entanglement. This remarkable effect occurs near half filling, where the concurrence becomes up to 15% larger than in the ordered system.Comment: 21 pages, 9 figure

Singular Lagrangian Systems on Jet Bundles

The jet bundle description of time-dependent mechanics is revisited. The constraint algorithm for singular Lagrangians is discussed and an exhaustive description of the constraint functions is given. By means of auxiliary connections we give a basis of constraint functions in the Lagrangian and Hamiltonian sides. An additional description of constraints is also given considering at the same time compatibility, stability and second-order condition problems. Finally, a classification of the constraints in first and second class is obtained using a cosymplectic geometry setting. Using the second class constraints, a Dirac bracket is introduced, extending the well-known construction by Dirac.Comment: 65 pages. LaTeX fil

Grain-size trends associated with sediment transport patterns in Cadiz Bay (southwest Iberian Peninsula)

En la zona infralitoral y de plataforma interna, las tendencias en los parámetros granulométricos permiten caracterizar ambientes antiguos y modernos, e identificar trayectorias de transporte de sedimentos mediante el análisis de las distribuciones granulométricas y el análisis factorial multivariante. En la bahía de Cádiz, las tendencias observadas en los parámetros granulométricos están controladas por los aportes de sedimentos finos, la configuración de la costa y las trayectorias de transporte en suspensión debidas a las corrientes de reflujo mareal. La asimetría es el parámetro principal en la identificación de tendencias granulométricas. Se han determinado tres tendencias que caracterizan los ambientes sedimentarios presentes: a) asimetrías muy positivas y distribuciones muy leptocúrticas indican un alto grado de madurez textural y retrabajamiento; b) tendencias hacia asimetrías negativas caracterizan ambientes intermareales de playa y permiten localizar ambientes paleolitorales; c) distribuciones simétricas y mal seleccionadas trazan las trayectorias permanentes de precipitación de sedimentos finos, mientras asimetrías más positivas, aumento del tamaño de grano y mejor selección marcan la extensión ocasional de las plumas de materia en suspensión.On the inner continental shelf and coastal environments, grain-size trends make it possible to characterise ancient and modern environments, and to identify net sediment transport patterns, using grain-size distributions and factorial multivariate analysis. In Cadiz Bay, grain-size trends are controlled by the contribution of fine sediments, coastal morphology and the suspended transport pathways due to the ebb-currents. The main parameter able to identify grain-size trends is skewness. Three trends were determined to characterise present-day sedimentary environments: a) very positively skewed sediments with leptokurtic distributions belong to deposits with a high degree of textural maturity and reworking; b) negatively skewed sediments characterise intertidal environments (foreshore), and also make it possible to localise palaeolittoral environments; c) symmetrical and poorly sorted distributions indicate the permanent fine-settling pathways, whereas positively skewed, coarser and better-sorted sediments point to the occasional extension of suspended matter plumes.Instituto Español de Oceanografí