Localized modes of binary mixtures of Bose-Einstein condensates in nonlinear optical lattices

The properties of the localized states of a two component Bose-Einstein condensate confined in a nonlinear periodic potential [nonlinear optical lattice] are investigated. We reveal the existence of new types of solitons and study their stability by means of analytical and numerical approaches. The symmetry properties of the localized states with respect to the NOL are also investigated. We show that nonlinear optical lattices allow the existence of bright soliton modes with equal symmetry in both components, bright localized modes of mixed symmetry type, as well as, dark-bright bound states and bright modes on periodic backgrounds. In spite of the quasi 1D nature of the problem, the fundamental symmetric localized modes undergo a delocalizing transition when the strength of the nonlinear optical lattice is varied. This transition is associated with the existence of an unstable solution, which exhibits a shrinking (decaying) behavior for slightly overcritical (undercritical) variations in the number of atoms.Comment: 13 pages, 14 figure

Quantum-tunneling dynamics of a spin-polarized Fermi gas in a double-well potential

We study the exact dynamics of a one-dimensional spin-polarized gas of fermions in a double-well potential at zero and finite temperature. Despite the system is made of non-interacting fermions, its dynamics can be quite complex, showing strongly aperiodic spatio-temporal patterns during the tunneling. The extension of these results to the case of mixtures of spin-polarized fermions in interaction with self-trapped Bose-Einstein condensates (BECs) at zero temperature is considered as well. In this case we show that the fermionic dynamics remains qualitatively similar to the one observed in absence of BEC but with the Rabi frequencies of fermionic excited states explicitly depending on the number of bosons and on the boson-fermion interaction strength. From this, the possibility to control quantum fermionic dynamics by means of Feshbach resonances is suggested.Comment: Accepted for publication in Phys. Rev.

Soliton ratchets induced by ac forces with harmonic mixing

The ratchet dynamics of a kink (topological soliton) of a dissipative sine-Gordon equation in the presence of ac forces with harmonic mixing (at least bi-harmonic) of zero mean is studied. The dependence of the kink mean velocity on system parameters is investigated numerically and the results are compared with a perturbation analysis based on a point particle representation of the soliton. We find that first order perturbative calculations lead to incomplete descriptions, due to the important role played by the soliton-phonon interaction in establishing the phenomenon. The role played by the temporal symmetry of the system in establishing soliton ratchets is also emphasized. In particular, we show the existence of an asymmetric internal mode on the kink profile which couples to the kink translational mode through the damping in the system. Effective soliton transport is achieved when the internal mode and the external force get phase locked. We find that for kinks driven by bi-harmonic drivers consisting of the superposition of a fundamental driver with its first odd harmonic, the transport arises only due to this {\it internal mode} mechanism, while for bi-harmonic drivers with even harmonic superposition, also a point-particle contribution to the drift velocity is present. The phenomenon is robust enough to survive the presence of thermal noise in the system and can lead to several interesting physical applications.Comment: 9 pages, 13 figure

Matter-wave 2D solitons in crossed linear and nonlinear optical lattices

It is demonstrated the existence of multidimensional matter-wave solitons in a crossed optical lattice (OL) with linear OL in the $x-$direction and nonlinear OL (NOL) in the $y-$direction, where the NOL can be generated by a periodic spatial modulation of the scattering length using an optically induced Feshbach resonance. In particular, we show that such crossed linear and nonlinear OL allows to stabilize two-dimensional (2D) solitons against decay or collapse for both attractive and repulsive interactions. The solutions for the soliton stability are investigated analytically, by using a multi-Gaussian variational approach (VA), with the Vakhitov-Kolokolov (VK) necessary criterion for stability; and numerically, by using the relaxation method and direct numerical time integrations of the Gross-Pitaevskii equation (GPE). Very good agreement of the results corresponding to both treatments is observed.Comment: 8 pages (two-column format), with 16 eps-files of 4 figure

A Study of the Differences between Classrooms Using a Meaning-Centered Approach and a Code-Centered Approach in the First Year Implementation of the California English-Language Arts Framework

The purpose of this descriptive study was to determine how a meaning-centered approach versus a code-centered approach affects student performance: (a) in the teaching of language arts; (b) in regular education classrooms containing low achieving, low socio-economic, multi-ethnic, and learning handicapped students; (c) in grades one, three and six; and (d) in the first year implementation of the California English-Language Arts Framework. This study focused on three interrelated dimensions of organizational change which are linked to student performance: curriculum materials, teacher behaviors, and organizational change processes. Eight research questions guided the examination of qualitative and quantitative data originating from teacher and principal interviews, teacher questionnaires, teacher meeting observations, classroom observations, and standardized test scores in language arts and reading of the student sample population, the school and the district. Some of the findings indicated that: 1. New language arts curriculum materials generated motivation and excitement. 2. Teachers continued to supplement the prescribed curriculum with materials they had previously found to be effective. 3. Students who received opportunities to use both a systematic skill program and inventive spelling appeared to reflect the greatest improvement in the subject of spelling on standardized tests. 4. Of the 11 instructional practices identified for examination, three practices consistently appeared to influence student performance: (a) instruction in both a systematic skill program and in an integrated literature program; (b) hearing literature read daily; (c) and daily writing activities. 5. Observations indicated that teachers\u27 instructional behaviors did not focus on transference of learning through the use of guided practice, generalization, or independent practice. 6. Teachers\u27 estimations of students\u27 progress seemed to correlate with achievement test results. 7. The percentage of multi-ethnic, low socio-economic, low achievement, and learning handicapped students in classrooms did not appear to make a difference in student performance. 8. There appeared to be a limited focus on minority languages and cultures in the curriculum materials and in classroom cooperative discussions. 9. The types of openness and bonding behaviors observed among organizational members did not appear to be effective in bringing about changes in teacher behaviors which would lead to better student performance. 10. Teachers\u27 degree of commitment to the language arts philosophy seemed to depend upon the level of achievement of their students on end of year standardized tests. 11. Reform implementation requires a revised focus on transformational leadership and organizational change processes. One recommendation emerging from this study is that organizations seeking to change must provide training and development which support the change process through demonstration, modeling, practice, correction, teaching, feedback, sharing and coaching in a collegial fashion. This study concludes with a series of implications, recommendations, and suggestions for further research which are needed to create change in literacy instructional practices

Thermal conductance of pressed aluminum and stainless steel contacts at liquid helium temperatures

The thermal conductance of aluminum and stainless steel 304 sample pairs with surface finishes ranging from 0.1 to 1.6 microns rms roughness was investigated over a temperature range from 1.6 to 6.0 k. The thermal conductance follows a simple power law function of temperature, with the exponent ranging from 0.5 to 2.25, increases asymptotically with increasing applied force, and exhibits an anomaly for surface finishes in the 0.4 micron region

Hypergeometric decomposition of symmetric K3 quartic pencils

We study the hypergeometric functions associated to five one-parameter deformations of Delsarte K3 quartic hypersurfaces in projective space. We compute all of their Picard--Fuchs differential equations; we count points using Gauss sums and rewrite this in terms of finite field hypergeometric sums; then we match up each differential equation to a factor of the zeta function, and we write this in terms of global L-functions. This computation gives a complete, explicit description of the motives for these pencils in terms of hypergeometric motives.Comment: 70 pages, minor revision, to appear in Research in the Mathematical Science

Compactons in Nonlinear Schr\"odinger Lattices with Strong Nonlinearity Management

The existence of compactons in the discrete nonlinear Schr\"odinger equation in the presence of fast periodic time modulations of the nonlinearity is demonstrated. In the averaged DNLS equation the resulting effective inter-well tunneling depends on modulation parameters {\it and} on the field amplitude. This introduces nonlinear dispersion in the system and can lead to a prototypical realization of single- or multi-site stable discrete compactons in nonlinear optical waveguide and BEC arrays. These structures can dynamically arise out of Gaussian or compactly supported initial data.Comment: 4 pages, 4 figure