Collective and single-particle excitations of a trapped Bose gas

The density of states of a Bose-condensed gas confined in a harmonic trap is investigated. The predictions of Bogoliubov theory are compared with those of Hartree-Fock theory and of the hydrodynamic model. We show that the Hartree-Fock scheme provides an excellent description of the excitation spectrum in a wide range of energy, revealing a major role played by single-particle excitations in these confined systems. The crossover from the hydrodynamic regime, holding at low energies, to the independent-particle regime is explicitly explored by studying the frequency of the surface mode as a function of their angular momentum. The applicability of the semiclassical approximation for the excited states is also discussed. We show that the semiclassical approach provides simple and accurate formulas for the density of states and the quantum depletion of the condensate.

Preisach modeling of hysteresis for a pseudoelastic Cu-Zn-Al single crystal

Stress-strain trajectories associated with pseudoelastic behavior of a Cu¿19.4 Zn¿13.1 Al (at.%) single crystal at room temperature have been determined experimentally. For a constant cross-head speed the trajectories and the associated hysteresis behavior are perfectly reproducible; the trajectories exhibit memory properties, dependent only on the values of return points, where transformation direction is reverted. An adapted version of the Preisach model for hysteresis has been implemented to predict the observed trajectories, using a set of experimental first¿order reversal curves as input data. Explicit formulas have been derived giving all trajectories in terms of this data set, with no adjustable parameters. Comparison between experimental and calculated trajectories shows a much better agreement for descending than for ascending paths, an indication of a dissymmetry between the dissipation mechanisms operative in forward and reverse directions of martensitic transformation.

Bifurcations and chaos in single-roll natural convection with low Prandtl number

Convective flows of a small Prandtl number fluid contained in a two-dimensional cavity subject to a lateral thermal gradient are numerically studied by using different techniques. The aspect ratio (length to height) is kept at around 2. This value is found optimal to make the flow most unstable while keeping the basic single-roll structure. Two cases of thermal boundary conditions on the horizontal plates are considered: perfectly conducting and adiabatic. For increasing Rayleigh numbers we find a transition from steady flow to periodic oscillations through a supercritical Hopf bifurcation that maintains the centrosymmetry of the basic circulation. For a Rayleigh number of about ten times that of the Hopf bifurcation the system initiates a complex scenario of bifurcations. In the conductive case these include a quasiperiodic route to chaos. In the adiabatic one the dynamics is dominated by the interaction of two Neimark-Sacker bifurcations of the basic periodic solutions, leading to the stable coexistence of three incommensurate frequencies, and finally to chaos. In all cases, the complex time-dependent behavior does not break the basic, single-roll structure.

Effects of thresholding level variation in fringe binarization of multiobject joint transform correlation

It is possible to improve the fringe binarization method of joint transform correlation by choosing a suitable threshold level.

Controlled-intensity detection peaks in a binary joint transform correlator

In multiobject pattern recognition the height of the correlation peaks should be controlled when the power spectrum of ajoint transform correlator is binarized. In this paper a method to predetermine the value of detection peaks is demonstrated. The technique is based on a frequency-variant threshold in order to remove the intraclass terms and on a suitable factor to normalize the binary joint power spectrum. Digital simulations and experimental hybrid implementation of this method were carried out.

Nonlinear filtering in object and Fourier space in a joint transform optical correlator: comparison and experimental realization

The use of different kinds of nonlinear filtering in a joint transform correlator are studied and compared. The study is divided into two parts, one corresponding to object space and the second to the Fourier domain of the joint power spectrum. In the first part, phase and inverse filters are computed; their inverse Fourier transforms are also computed, thereby becoming the reference in the object space. In the Fourier space, the binarization of the power spectrum is realized and compared with a new procedure for removing the spatial envelope. All cases are simulated and experimentally implemented by a compact joint transform correlator.

Ultraviolet optical and microstructural properties of MgF2 and LaF3 coatings deposited by ion-beam sputtering and boat and electron-beam evaporation

Single layers of MgF2 and LaF3 were deposited upon superpolished fused-silica and CaF2 substrates by ion-beam sputtering (IBS) as well as by boat and electron beam (e-beam) evaporation and were characterized by a variety of complementary analytical techniques. Besides undergoing photometric and ellipsometric inspection, the samples were investigated at 193 and 633 nm by an optical scatter measurement facility. The structural properties were assessed with atomic-force microscopy, x-ray diffraction, TEM techniques that involved conventional thinning methods for the layers. For measurement of mechanical stress in the coatings, special silicon substrates were coated and analyzed. The dispersion behavior of both deposition materials, which was determined on the basis of various independent photometric measurements and data reduction techniques, is in good agreement with that published in the literature and with the bulk properties of the materials. The refractive indices of the MgF2 coatings ranged from 1.415 to 1.440 for the wavelength of the ArF excimer laser (193 nm) and from 1.435 to 1.465 for the wavelength of the F2 excimer laser (157 nm). For single layers of LaF3 the refractive indices extended from 1.67 to 1.70 at 193 nm to ~1.80 at 157 nm. The IBS process achieves the best homogeneity and the lowest surface roughness values (close to 1 nmrms) of the processes compared in the joint experiment. In contrast to MgF2 boat and e-beam evaporated coatings, which exhibit tensile mechanical stress ranging from 300 to 400 MPa, IBS coatings exhibit high compressive stress of as much as 910 MPa. A similar tendency was found for coating stress in LaF3 single layers. Experimental results are discussed with respect to the microstructural and compositional properties as well as to the surface topography of the coatings.

Reduction of the effect of aberrations in a joint transform correlator

We report the study of the influence of optical aberrations in a joint-transform correlator: The wave aberration of the optical system is computed from data obtained by ray tracing. Three situations are explored: We consider the aberration only in the first diffraction stage (generation of power spectrum), then only in the second (transformation of the power spectrum into correlation), and finally in both stages simultaneously. The results show that the quality of the correlation is determined mostly by the aberrations of the first diffraction stage and that we can optimize the setup by moving the cameras along the optical axis to a suitable position. The good agreement between the predicted data and the experimental results shows that the method explains well the behavior of optical diffraction systems when aberrations are taken into account.

Kerr measurements on single-domain SrRuO3 thin films

We report on the magneto-optical measurements of an epitaxial SrRuO3 film grown on SrTiO3 (0 0 1), which previously was determined to be single domain orientated by x-ray diffraction and Raman spectroscopy techniques. Our experiments reveal a large Kerr rotation, which reaches a maximum value of about 0.5° at low temperature. By measuring magnetic hysteresis loops at different temperatures, we determined the temperature dependence of the Kerr rotation in the polar configuration. Values of the anisotropic magnetoresistance ~ 20% have been measured. These values are remarkably higher than those of other metallic oxides such as manganites. This striking difference can be attributed to the strong spin-orbit interaction of the Ru 4d ion in the SrRuO3 compound.

Crystal defects and spin tunneling in single crystals of Mn12 clusters

The question addressed in this paper is that of the influence of the density of dislocations on the spin tunneling in Mn12 clusters. We have determined the variation in the mosaicity of fresh and thermally treated single crystals of Mn12 by analyzing the widening of low angle x-ray diffraction peaks. It has also been well established from both isothermal magnetization and relaxation experiments that there is a broad distribution of tunneling rates which is shifted to higher rates when the density of dislocations increases.

Occupancy of a single site by many random walkers

We consider an infinite number of noninteracting lattice random walkers with the goal of determining statistical properties of the time, out of a total time T, that a single site has been occupied by n random walkers. Initially the random walkers are assumed uniformly distributed on the lattice except for the target site at the origin, which is unoccupied. The random-walk model is taken to be a continuous-time random walk and the pausing-time density at the target site is allowed to differ from the pausing-time density at other sites. We calculate the dependence of the mean time of occupancy by n random walkers as a function of n and the observation time T. We also find the variance for the cumulative time during which the site is unoccupied. The large-T behavior of the variance differs according as the random walk is transient or recurrent. It is shown that the variance is proportional to T at large T in three or more dimensions, it is proportional to T3/2 in one dimension and to TlnT in two dimensions.

Metastable liquid-liquid phase transition in a single-component system with only one crystal phase and no density anomaly

We investigate the phase behavior of a single-component system in three dimensions with spherically-symmetric, pairwise-additive, soft-core interactions with an attractive well at a long distance, a repulsive soft-core shoulder at an intermediate distance, and a hard-core repulsion at a short distance, similar to potentials used to describe liquid systems such as colloids, protein solutions, or liquid metals. We showed [Nature (London) 409, 692 (2001)] that, even with no evidence of the density anomaly, the phase diagram has two first-order fluid-fluid phase transitions, one ending in a gas¿low-density-liquid (LDL) critical point, and the other in a gas¿high-density-liquid (HDL) critical point, with a LDL-HDL phase transition at low temperatures. Here we use integral equation calculations to explore the three-parameter space of the soft-core potential and perform molecular dynamics simulations in the interesting region of parameters. For the equilibrium phase diagram, we analyze the structure of the crystal phase and find that, within the considered range of densities, the structure is independent of the density. Then, we analyze in detail the fluid metastable phases and, by explicit thermodynamic calculation in the supercooled phase, we show the absence of the density anomaly. We suggest that this absence is related to the presence of only one stable crystal structure.

Quantum tunneling of magnetization in single domain particles

We present a study of the magnetic relaxation of several ferrofluids composed of particles of about 40 Å in diameter (Fe3O4FeC, CoFe2O4). Our key observation is a nonthermal character of the relaxation below 3 K for the CoFe2O4 ferrofluid and below 1 K for the FeC ferrofluid. The crossover temperature from thermal to nonthermal (quantum) regime is in accordance with theoretical suggestions of macroscopic quantum tunneling of magnetization in single doma in particles