X-ray laser pulses at the Fourier transform limit

The temporal output of a Ni-like Ag x-ray laser of wavelength 13.9 nm has been recorded using a streak camera with ultrashort (700 fs) temporal resolution. We present a model to calculate the degree of coherence and Fourier transform limit of x-ray laser pulses produced by amplified spontaneous emission and relate the results from the model to previous interferometric measurements of the coherence length of the same Ni-like Ag x-ray laser and our measured duration of temporal output. Our modeling shows that the interferometer and streak camera results are consistent and close to the Fourier transform limit at longer gain medium lengths

Sedimentology and kinematics of a large, retrogressive growth-fault system in Upper Carboniferous deltaic sediments, western Ireland

Growth faulting is a common feature of many deltaic environments and is vital in determining local sediment dispersal and accumulation, and hence in controlling the resultant sedimentary facies distribution and architecture. Growth faults occur on a range of scales, from a few centimetres to hundreds of metres, with the largest growth faults frequently being under-represented in outcrops that are often smaller than the scale of feature under investigation. This paper presents data from the exceptionally large outcrops of the Cliffs of Moher, western Ireland, where a growth-fault complex affects strata up to 60 m in thickness and extends laterally for 3 km. Study of this Namurian (Upper Carboniferous) growth-fault system enables the relationship between growth faulting and sedimentation to be detailed and permits reconstruction of the kinematic history of faulting. Growth faulting was initiated with the onset of sandstone deposition on a succession of silty mudstones that overlie a thin, marine shale. The decollement horizon developed at the top of the marine shale contact for the first nine faults, by which time aggradation in the hangingwall exceeded 60 m in thickness. After this time, failure planes developed at higher stratigraphic levels and were associated with smaller scale faults. The fault complex shows a dominantly landward retrogressive movement, in which only one fault was largely active at any one time. There is no evidence of compressional features at the base of the growth faults, thus suggesting open-ended slides, and the faults display both disintegrative and non-disintegrative structure. Thin-bedded, distal mouth bar facies dominate the hangingwall stratigraphy and, in the final stages of growth-fault movement, erosion of the crests of rollover structures resulted in the highest strata being restricted to the proximity of the fault. These upper erosion surfaces on the fault scarp developed erosive chutes that were cut parallel to flow and are downlapped by the distal hangingwall strata of younger growth faults

Order Parameter at the Boundary of a Trapped Bose Gas

Through a suitable expansion of the Gross-Pitaevskii equation near the classical turning point, we obtain an explicit solution for the order parameter at the boundary of a trapped Bose gas interacting with repulsive forces. The kinetic energy of the system, in terms of the classical radius $R$ and of the harmonic oscillator length $a_{_{HO}}$, follows the law $E_{kin}/N \propto R^{-2} [\log (R/a_{_{HO}}) + \hbox{const.}]$, approaching, for large $R$, the results obtained by solving numerically the Gross-Pitaevskii equation. The occurrence of a Josephson-type current in the presence of a double trap potential is finally discussed.Comment: 11 pages, REVTEX, 4 figures (uuencoded-gzipped-tar file) also available at http://anubis.science.unitn.it/~dalfovo/papers/papers.htm

Condensate fraction and critical temperature of a trapped interacting Bose gas

By using a mean field approach, based on the Popov approximation, we calculate the temperature dependence of the condensate fraction of an interacting Bose gas confined in an anisotropic harmonic trap. For systems interacting with repulsive forces we find a significant decrease of the condensate fraction and of the critical temperature with respect to the predictions of the non-interacting model. These effects go in the opposite direction compared to the case of a homogeneous gas. An analytic result for the shift of the critical temperature holding to first order in the scattering length is also derived.Comment: 8 pages, REVTEX, 2 figures, also available at http://anubis.science.unitn.it/~oss/bec/BEC.htm

Bosons in anisotropic traps: ground state and vortices

We solve the Gross-Pitaevskii equations for a dilute atomic gas in a magnetic trap, modeled by an anisotropic harmonic potential. We evaluate the wave function and the energy of the Bose Einstein condensate as a function of the particle number, both for positive and negative scattering length. The results for the transverse and vertical size of the cloud of atoms, as well as for the kinetic and potential energy per particle, are compared with the predictions of approximated models. We also compare the aspect ratio of the velocity distribution with first experimental estimates available for $^{87}$Rb. Vortex states are considered and the critical angular velocity for production of vortices is calculated. We show that the presence of vortices significantly increases the stability of the condensate in the case of attractive interactions.Comment: 22 pages, REVTEX, 8 figures available upon request or at http://anubis.science.unitn.it/~dalfovo/papers/papers.htm

A Pinned Polymer Model of Posture Control

A phenomenological model of human posture control is posited. The dynamics are modelled as an elastically pinned polymer under the influence of noise. The model accurately reproduces the two-point correlation functions of experimental posture data and makes predictions for the response function of the postural control system. The physiological and clinical significance of the model is discussed.Comment: uuencoded post script file, 17 pages with 3 figure

Conserving and Gapless Approximations for an Inhomogeneous Bose Gas at Finite Temperatures

We derive and discuss the equations of motion for the condensate and its fluctuations for a dilute, weakly interacting Bose gas in an external potential within the self--consistent Hartree--Fock--Bogoliubov (HFB) approximation. Account is taken of the depletion of the condensate and the anomalous Bose correlations, which are important at finite temperatures. We give a critical analysis of the self-consistent HFB approximation in terms of the Hohenberg--Martin classification of approximations (conserving vs gapless) and point out that the Popov approximation to the full HFB gives a gapless single-particle spectrum at all temperatures. The Beliaev second-order approximation is discussed as the spectrum generated by functional differentiation of the HFB single--particle Green's function. We emphasize that the problem of determining the excitation spectrum of a Bose-condensed gas (homogeneous or inhomogeneous) is difficult because of the need to satisfy several different constraints.Comment: plain tex, 19 page

Testing quantum correlations in a confined atomic cloud by scattering fast atoms

We suggest measuring one-particle density matrix of a trapped ultracold atomic cloud by scattering fast atoms in a pure momentum state off the cloud. The lowest-order probability of the inelastic process, resulting in a pair of outcoming fast atoms for each incoming one, turns out to be given by a Fourier transform of the density matrix. Accordingly, important information about quantum correlations can be deduced directly from the differential scattering cross-section. A possible design of the atomic detector is also discussed.Comment: 5 RevTex pages, no figures, submitted to PR

Stability of the trapped nonconservative Gross-Pitaevskii equation with attractive two-body interaction

The dynamics of a nonconservative Gross-Pitaevskii equation for trapped atomic systems with attractive two-body interaction is numerically investigated, considering wide variations of the nonconservative parameters, related to atomic feeding and dissipation. We study the possible limitations of the mean field description for an atomic condensate with attractive two-body interaction, by defining the parameter regions where stable or unstable formation can be found. The present study is useful and timely considering the possibility of large variations of attractive two-body scattering lengths, which may be feasible in recent experiments.Comment: 6 pages, 5 figures, submitted to Physical Review

Spectral method for the time-dependent Gross-Pitaevskii equation with a harmonic trap

We study the numerical resolution of the time-dependent Gross-Pitaevskii equation, a non-linear Schroedinger equation used to simulate the dynamics of Bose-Einstein condensates. Considering condensates trapped in harmonic potentials, we present an efficient algorithm by making use of a spectral Galerkin method, using a basis set of harmonic oscillator functions, and the Gauss-Hermite quadrature. We apply this algorithm to the simulation of condensate breathing and scissors modes.Comment: 23 pages, 5 figure