Mobile Bipolarons in the Adiabatic Holstein-Hubbard Model in 1 and 2 dimensions

The bound states of two electrons in the adiabatic Holstein-Hubbard model are studied numerically in one and two dimensions from the anticontinuous limit. This model involves a competition between a local electron-phonon coupling (with a classical lattice) which tends to form pairs of electrons and the repulsive Hubbard interaction $U \geq 0$ which tends to break them. In 1D, the ground-state always consists in a pair of localized polarons in a singlet state. They are located at the same site for U=0. Increasing U, there is a first order transition at which the bipolaron becomes a spin singlet pair of two polarons bounded by a magnetic interaction. The pinning mode of the bipolaron soften in the vicinity of this transition leading to a higher mobility of the bipolaron which is tested numerically. In 2D, and for any $U$, the electron-phonon coupling needs to be large enough in order to form small polarons or bipolarons instead of extended electrons. We calculate the phase diagram of the bipolaron involving first order transitions lines with a triple point. A pair of polarons can form three types of bipolarons: a) on a single site at small $U$, b) a spin singlet state on two nearest neighbor sites for larger $U$ as in 1D and c) a new intermediate state obtained as the resonant combination of four 2-sites singlet states sharing a central site, called quadrisinglet. The breathing and pinning internal modes of bipolarons in 2D generally only weakly soften and thus, they are practically not mobile. On the opposite, in the vicinity of the triple point involving the quadrisinglet, both modes exhibit a significant softening. However, it was not sufficient for allowing the existence of a classical mobile bipolaron (at least in that model)

A low dimensional dynamical system for the wall layer

Low dimensional dynamical systems which model a fully developed turbulent wall layer were derived.The model is based on the optimally fast convergent proper orthogonal decomposition, or Karhunen-Loeve expansion. This decomposition provides a set of eigenfunctions which are derived from the autocorrelation tensor at zero time lag. Via Galerkin projection, low dimensional sets of ordinary differential equations in time, for the coefficients of the expansion, were derived from the Navier-Stokes equations. The energy loss to the unresolved modes was modeled by an eddy viscosity representation, analogous to Heisenberg's spectral model. A set of eigenfunctions and eigenvalues were obtained from direct numerical simulation of a plane channel at a Reynolds number of 6600, based on the mean centerline velocity and the channel width flow and compared with previous work done by Herzog. Using the new eigenvalues and eigenfunctions, a new ten dimensional set of ordinary differential equations were derived using five non-zero cross-stream Fourier modes with a periodic length of 377 wall units. The dynamical system was integrated for a range of the eddy viscosity prameter alpha. This work is encouraging

Magnetotail changes in relation to the solar wind magnetic field and magnetospheric substorms

An attempt is made to understand some of the magnetotail dynamics by using simultaneous observations from several satellites: Explorers 33 and 35 in the solar wind, IMP 4 in the near magnetotail (30 RE), ATS 1, and OGO 5 in the magnetosphere. It was observed that in the main lobes of the tail the magnetic field increases slowly when the interplanetary magnetic field turns southward, and can decrease slowly after a substorm. The plasma sheet changes indicate a thinning when the interplanetary magnetic field turns southward and an expansion when it turns northward. When combined with the plasma sheet expansion, which has been observed to follow a substorm, these results allow a schematic view of the relations between the changes in the orientation of the solar wind magnetic field, the substorms, and the changes in the tail parameters to be developed

Surface spin-flop phases and bulk discommensurations in antiferromagnets

Phase diagrams as a function of anisotropy D and magnetic field H are obtained for discommensurations and surface states for a model antiferromagnet in which $H$ is parallel to the easy axis. The surface spin-flop phase exists for all $D$. We show that there is a region where the penetration length of the surface spin-flop phase diverges. Introducing a discommensuration of even length then becomes preferable to reconstructing the surface. The results are used to clarify and correct previous studies in which discommensurations have been confused with genuine surface spin-flop states.Comment: 4 pages, RevTeX, 2 Postscript figure

Correlated bosons in a one-dimensional optical lattice: Effects of the trapping potential and of quasiperiodic disorder

We investigate the effect of the trapping potential on the quantum phases of strongly correlated ultracold bosons in one-dimensional periodic and quasiperiodic optical lattices. By means of a decoupling meanfield approach, we characterize the ground state of the system and its behavior under variation of the harmonic trapping, as a function of the total number of atoms. For a small atom number the system shows an incompressible Mott-insulating phase, as the size of the cloud remains unaffected when the trapping potential is varied. When the quasiperiodic potential is added the system develops a metastable-disordered phase which is neither compressible nor Mott insulating. This state is characteristic of quasidisorder in the presence of a strong trapping potential.Comment: Accepted for publication in PR

Localization of a Bose-Einstein condensate vortex in a bichromatic optical lattice

By numerical simulation of the time-dependent Gross-Pitaevskii equation we show that a weakly interacting or noninteracting Bose-Einstein condensate (BEC) vortex can be localized in a three-dimensional bichromatic quasi-periodic optical-lattice (OL) potential generated by the superposition of two standing-wave polarized laser beams with incommensurate wavelengths. This is a generalization of the localization of a BEC in a one-dimensional bichromatic OL as studied in a recent experiment [Roati et al., Nature 453, 895 (2008)]. We demonstrate the stability of the localized state by considering its time evolution in the form of a stable breathing oscillation in a slightly altered potential for a large period of time. {Finally, we consider the localization of a BEC in a random 1D potential in the form of several identical repulsive spikes arbitrarily distributed in space

Mass mortality and extraterrestrial impacts

The discovery of iridium enrichment at the Cretaceous/Tertiary boundary resulted in formulation of hypothesis of a cometary or asteroid impact as the cause of the biological extinctions at this boundary. Subsequent discoveries of geochemical anomalies at major stratigraphic boundaries like the Precambrian/Cambrian, Permian/Triassic, Middle/Late Jurassic, resulted in the application of similar extraterrestrial impact theories to explain biological changes at these boundaries. Until recently the major physical evidence, as is the location of the impact crater site, to test the impact induced biological extinction was lacking. The diameter of such a crater would be in the range of 60 to 100 km. The recent discovery of the first impact crater in the ocean provide the first opportunity to test the above theory. The crater, named Montagnais and located on the outer shelf off Nova Scotia, Canada, has a minimum diameter of 42 km, with some evidence to a diameter of more than 60 km. At the Montagnais impact site, micropaleontological analysis of the uppermost 80 m of the fall-back breccia represented by a mixture of pre-impact sediments and basement rocks which fills the crater and of the basal 50 m of post-impact marine sediments which overly the impact deposits, revealed presence of diversified foraminiferal and nannoplankton assemblages. The sediments which are intercalated within the uppermost part of the fall-back breccia, had to be deposited before the meteorite impact. The post-impact deposits were laid down almost immediately after the impact as also supported by the micropaleontological data. In conclusion, micropaleontological studies of sediments from the first submarine impact crater site identified in the ocean did not reveal any mass extinction or significant biological changes at the impact site or in the proximal deep ocean basin

Effects of interaction on the diffusion of atomic matter waves in one-dimensional quasi-periodic potentials

We study the behaviour of an ultracold atomic gas of bosons in a bichromatic lattice, where the weaker lattice is used as a source of disorder. We numerically solve a discretized mean-field equation, which generalizes the one-dimensional Aubry-Andr\`e model for particles in a quasi-periodic potential by including the interaction between atoms. We compare the results for commensurate and incommensurate lattices. We investigate the role of the initial shape of the wavepacket as well as the interplay between two competing effects of the interaction, namely self-trapping and delocalization. Our calculations show that, if the condensate initially occupies a single lattice site, the dynamics of the interacting gas is dominated by self-trapping in a wide range of parameters, even for weak interaction. Conversely, if the diffusion starts from a Gaussian wavepacket, self-trapping is significantly suppressed and the destruction of localization by interaction is more easily observable

Localization of a Bose-Einstein condensate in a bichromatic optical lattice

By direct numerical simulation of the time-dependent Gross-Pitaevskii equation we study different aspects of the localization of a non-interacting ideal Bose-Einstein condensate (BEC) in a one-dimensional bichromatic quasi-periodic optical-lattice potential. Such a quasi-periodic potential, used in a recent experiment on the localization of a BEC [Roati et al., Nature 453, 895 (2008)], can be formed by the superposition of two standing-wave polarized laser beams with different wavelengths. We investigate the effect of the variation of optical amplitudes and wavelengths on the localization of a non-interacting BEC. We also simulate the non-linear dynamics when a harmonically trapped BEC is suddenly released into a quasi-periodic potential, {as done experimentally in a laser speckle potential [Billy et al., Nature 453, 891 (2008)]$ We finally study the destruction of the localization in an interacting BEC due to the repulsion generated by a positive scattering length between the bosonic atoms.Comment: 8 page