Conserving Approximations in Time-Dependent Density Functional Theory

In the present work we propose a theory for obtaining successively better approximations to the linear response functions of time-dependent density or current-density functional theory. The new technique is based on the variational approach to many-body perturbation theory (MBPT) as developed during the sixties and later expanded by us in the mid nineties. Due to this feature the resulting response functions obey a large number of conservation laws such as particle and momentum conservation and sum rules. The quality of the obtained results is governed by the physical processes built in through MBPT but also by the choice of variational expressions. We here present several conserving response functions of different sophistication to be used in the calculation of the optical response of solids and nano-scale systems.Comment: 11 pages, 4 figures, revised versio

Age, Metallicity, and the Distance to the Magellanic Clouds From Red Clump Stars

We show that the luminosity dependence of the red clump stars on age and metallicity can cause a difference of up to < ~0.6 mag in the mean absolute I magnitude of the red clump between different stellar populations. We show that this effect may resolve the apparent ~0.4 mag discrepancy between red clump-derived distance moduli to the Magellanic Clouds and those from, e.g., Cepheid variables. Taking into account the population effects on red clump luminosity, we determine a distance modulus to the LMC of 18.36 +/- 0.17 mag, and to the SMC of 18.82 +/- 0.20 mag. Our alternate red clump LMC distance is consistent with the value (m-M){LMC} = 18.50 +/- 0.10 adopted by the HST Cepheid Key Project. We briefly examine model predictions of red clump luminosity, and find that variations in helium abundance and core mass could bring the Clouds closer by some 0.10--0.15 mag, but not by the ~0.4 mag that would result from setting the mean absolute I-magnitude of the Cloud red clumps equal to the that of the Solar neighborhood red clump.Comment: Accepted for publication in The Astrophysical Journal Letters, AASTeX 4.0, 10 pages, 1 postscript figur

Spin-polarized stable phases of the 2-D electron fluid at finite temperatures

The Helmholtz free energy F of the interacting 2-D electron fluid is calculated nonperturbatively using a mapping of the quantum fluid to a classical Coulomb fluid [Phys. Rev. Letters, vol. 87, 206404 (2001)]. For density parameters rs such that rs<~25, the fluid is unpolarized at all temperatures t=T/EF where EF is the Fermi energy. For lower densities, the system becomes fully spin polarized for t<~0.35, and partially polarized for 0.35<t< 2, depending on the density. At rs ~25-30, and t ~0.35, an ''ambispin'' phase where F is almost independent of the spin polarization is found. These results support recent claims, based on quantum Monte Carlo results, for a stable, fully spin-polarized fluid phase at T = 0 for rs larger than about 25-26.Comment: Latex manuscript (4-5 pages) and two postscript figures; see also http://nrcphy1.phy.nrc.ca/ims/qp/chandre/chnc

Waiting and Residence Times of Brownian Interface Fluctuations

We report on the residence times of capillary waves above a given height $h$ and on the typical waiting time in between such fluctuations. The measurements were made on phase separated colloid-polymer systems by laser scanning confocal microscopy. Due to the Brownian character of the process, the stochastics vary with the chosen measurement interval $\Delta t$. In experiments, the discrete scanning times are a practical cutoff and we are able to measure the waiting time as a function of this cutoff. The measurement interval dependence of the observed waiting and residence times turns out to be solely determined by the time dependent height-height correlation function $g(t)$. We find excellent agreement with the theory presented here along with the experiments.Comment: 5 figure

A recurrent neural network with ever changing synapses

A recurrent neural network with noisy input is studied analytically, on the basis of a Discrete Time Master Equation. The latter is derived from a biologically realizable learning rule for the weights of the connections. In a numerical study it is found that the fixed points of the dynamics of the net are time dependent, implying that the representation in the brain of a fixed piece of information (e.g., a word to be recognized) is not fixed in time.Comment: 17 pages, LaTeX, 4 figure

Leading-edge vortices elevate lift of autorotating plant seeds

As they descend, the autorotating seeds of maples and some other trees generate unexpectedly high lift, but how they attain this elevated performance is unknown. To elucidate the mechanisms responsible, we measured the three-dimensional flow around dynamically scaled models of maple and hornbeam seeds. Our results indicate that these seeds attain high lift by generating a stable leading-edge vortex (LEV) as they descend. The compact LEV, which we verified on real specimens, allows maple seeds to remain in the air more effectively than do a variety of nonautorotating seeds. LEVs also explain the high lift generated by hovering insects, bats, and possibly birds, suggesting that the use of LEVs represents a convergent aerodynamic solution in the evolution of flight performance in both animals and plants

Time correlations in a confined magnetized free-electron gas

The time-dependent pair correlation functions for a degenerate ideal quantum gas of charged particles in a uniform magnetic field are studied on the basis of equilibrium statistics. In particular, the influence of a flat hard wall on the correlations is investigated, both for a perpendicular and a parallel orientation of the wall with respect to the field. The coherent and incoherent parts of the time-dependent structure function in position space are determined from an expansion in terms of the eigenfunctions of the one-particle Hamiltonian. For the bulk of the system, the intermediate scattering function and the dynamical structure factor are derived by taking successive Fourier transforms. In the vicinity of the wall the time-dependent coherent structure function is found to decay faster than in the bulk. For coinciding positions near the wall the form of the structure function turns out to be independent of the orientation of the wall. Numerical results are shown to corroborate these findings.Comment: 25 pages, 14 figures, to be published in Journal of Physics

The Equation of State and the Hugoniot of Laser Shock-Compressed Deuterium

The equation of state and the shock Hugoniot of deuterium are calculated using a first-principles approach, for the conditions of the recent shock experiments. We use density functional theory within a classical mapping of the quantum fluids [ Phys. Rev. Letters, {\bf 84}, 959 (2000) ]. The calculated Hugoniot is close to the Path-Integral Monte Carlo (PIMC) result. We also consider the {\it quasi-equilibrium} two-temperature case where the Deuterons are hotter than the electrons; the resulting quasi-equilibrium Hugoniot mimics the laser-shock data. The increased compressibility arises from hot $D^+-e$ pairs occuring close to the zero of the electron chemical potential.Comment: Four pages; One Revtex manuscript, two postscipt figures; submitted to PR

Observation of Nonspreading Wave Packets in an Imaginary Potential

We propose and experimentally demonstrate a method to prepare a nonspreading atomic wave packet. Our technique relies on a spatially modulated absorption constantly chiseling away from an initially broad de Broglie wave. The resulting contraction is balanced by dispersion due to Heisenberg's uncertainty principle. This quantum evolution results in the formation of a nonspreading wave packet of Gaussian form with a spatially quadratic phase. Experimentally, we confirm these predictions by observing the evolution of the momentum distribution. Moreover, by employing interferometric techniques, we measure the predicted quadratic phase across the wave packet. Nonspreading wave packets of this kind also exist in two space dimensions and we can control their amplitude and phase using optical elements.Comment: 4 figure