Collective excitations of trapped Bose-Einstein condensates in the energy and time domains

A time-dependent method for calculating the collective excitation frequencies and densities of a trapped, inhomogeneous Bose-Einstein condensate with circulation is presented. The results are compared with time-independent solutions of the Bogoliubov-de Gennes equations. The method is based on time-dependent linear-response theory combined with spectral analysis of moments of the excitation modes of interest. The technique is straightforward to apply, extremely efficient in our implementation with parallel fast Fourier transform methods, and produces highly accurate results. For high dimensionality or low symmetry the time-dependent approach is a more practical computational scheme and produces accurate and reliable data. The method is suitable for general trap geometries, condensate flows and condensates permeated with defects and vortex structures.

Phase behavior of mixtures of colloidal platelets and nonadsorbing polymers

The phase behavior of a model system of colloidal platelets and nonadsorbing polymers is studied using computer simulations and perturbation theory. The equation of state for the pure platelet reference system is obtained by Monte Carlo simulations, and the free volume fraction accessible to polymers is measured by a trial insertion method. The free volume fraction is also calculated using scaled particle theory. Subsequently, the phase diagram for platelet-polymer mixtures is calculated. For a platelet aspect ratio L/D=0.1 and a polymer to platelet size ratio d/D>0.2, we observe coexistence between two isotropic phases with different densities. For smaller polymers d/D

Calculation of gamma spectra for positron annihilation on molecules

Calculations of gamma spectra for positron annihilation for a selection of molecules, including methane and its fluoro-substitutes, ethane, propane, butane and benzene are presented. The contribution to the ?-spectra from individual molecular orbitals is obtained from electron momentum distributions calculated using the density functional theory (DFT) based B3LYP/TZVP model. For positrons thermalised to room temperature, the calculation, in its simplest form, effectively treats the positron as a plane wave and gives positron annihilation ?-spectra linewidths that are broader (30-40%) than experiment, although the main chemical trends are reproduced. The main physical reason for this is the neglect of positron repulsion from the nuclei. We show that this effect can be incorporated through momentum-dependent correction factors, determined from positron-atom calculations, e.g., many-body perturbation theory. Inclusion of these factors in the calculation gives linewidths that are in improved agreement with experiment.

Partial and total multiphoton detachment rates for H- in a perturbative B-spline-based approach

An ab initio approach has been applied to study multiphoton detachment rates for the negative hydrogen ion in the lowest nonvanishing order of perturbation theory. The approach is based on the use of B splines allowing an accurate treatment of the electronic repulsion. Total detachment rates have been determined for two- to six-photon processes as well as partial rates for detachment into the different final symmetries. It is shown that B-spline expansions can yield accurate continuum and bound-state wave functions in a very simple manner. The calculated total rates for two- and three-photon detachment are in good agreement with other perturbative calculations. For more than three-photon detachment little information has been available before now. While the total cross sections show little structure, a fair amount of structure is predicted in the partial cross sections. In the two-photon process, it is shown that the detached electrons mainly have s character. For four- and six-photon processes, the contribution from the d channel is the most important. For three- and five-photon processes p electrons dominate the electron emission spectrum. Detachment rates for s and p electrons show minima as a function of photon energy. © 1994 The American Physical Society.

yambo: An ab initio tool for excited state calculations

yambo is an ab initio code for calculating quasiparticle energies and optical properties of electronic systems within the framework of many-body perturbation theory and time-dependent density functional theory. Quasiparticle energies are calculated within the GW approximation for the self-energy. Optical properties are evaluated either by solving the Bethe-Salpeter equation or by using the adiabatic local density approximation. yambo is a plane-wave code that, although particularly suited for calculations of periodic bulk systems, has been applied to a large variety of physical systems. yambo relies on efficient numerical techniques devised to treat systems with reduced dimensionality, or with a large number of degrees of freedom. The code has a user-friendly command-line based interface, flexible 110 procedures and is interfaced to several publicly available density functional ground-state codes.

Shape corrections to exchange-correlation potentials by gradient-regulated seamless connection of model potentials for inner and outer region

Shape corrections to the standard approximate Kohn-Sham exchange-correlation (xc) potentials are considered with the aim to improve the excitation energies (especially for higher excitations) calculated with time-dependent density functional perturbation theory. A scheme of gradient-regulated connection (GRAC) of inner to outer parts of a model potential is developed. Asymptotic corrections based either on the potential of Fermi and Amaldi or van Leeuwen and Baerends (LB) are seamlessly connected to the (shifted) xc potential of Becke and Perdew (BP) with the GRAC procedure, and are employed to calculate the vertical excitation energies of the prototype molecules N-2, CO, CH2O, C2H4, C5NH5, C6H6, Li-2, Na-2, K-2. The results are compared with those of the alternative interpolation scheme of Tozer and Handy as well as with the results of the potential obtained with the statistical averaging of (model) orbital potentials. Various asymptotically corrected potentials produce high quality excitation energies, which in quite a few cases approach the benchmark accuracy of 0.1 eV for the electronic spectra. Based on these results, the potential BP-GRAC-LB is proposed for molecular response calculations, which is a smooth potential and a genuine "local" density functional with an analytical representation. (C) 2001 American Institute of Physics.

Magnetic properties of copper hexadecaphthalocyanine (F16CuPc) thin films and powders

The structural and magnetic properties of F16CuPc thin films and powder, including x-ray diffraction (XRD), superconducting quantum interference device (SQUID) magnetometry, and theoretical modelling of exchange interactions are reported. Analysis of XRD from films, with thickness ranging between 100 and 160 nm, deposited onto Kapton and a perylene-3,4,9,10-tetracarboxylic-3,4,9,10-dianhydride (PTCDA) interlayer shows that the stacking angle (defined in the text) of the film is independent of the thickness, but that the texture is modified by both film thickness and substrate chemistry. The SQUID measurements suggest that all samples are paramagnetic, a result that is confirmed by our theoretical modelling including density functional theory calculations of one-dimensional molecular chains and Green's function perturbation theory calculations for a molecular dimer. By investigating theoretically a range of different geometries, we predict that the maximum possible exchange interaction between F16CuPc molecules is twice as large as that in unfluorinated copper-phthalocyanine (CuPc). This difference arises from the smaller intermolecular spacing in F16CuPc. Our density functional theory calculation for isolated F16CuPc molecule also shows that the energy levels of Kohn-Sham orbitals are rigidly shifted similar to 1 eV lower in F16CuPc compared to CuPc without a significant modification of the intramolecular spin physics, and that therefore the two molecules provide a suitable platform for independently varying magnetism and charge transport. 

Anisotropy parameters in two-color two-photon above-threshold ionization

We employ the time-dependent R-matrix (TDRM) method to calculate anisotropy parameters for positive and negative sidebands of selected harmonics generated by two-color two-photon above-threshold ionization of argon. We consider odd harmonics of an 800-nm field ranging from the 13th to 19th harmonic, overlapped by a fundamental 800-nm IR field. The anisotropy parameters obtained using the TDRM method are compared with those obtained using a second-order perturbation theory with a model potential approach and a soft photon approximation approach. Where available, a comparison is also made to published experimental results. All three theoretical approaches provide similar values for anisotropy parameters. The TDRM approach obtains values that are closest to published experimental values. At high photon energies, the differences between each of the theoretical methods become less significant.

Thermodynamic Properties of Dichloromethane, Bromochloromethane, and Dibromomethane under Elevated Pressure: Experimental Results and SAFT-VR Mie Predictions

The speeds of sound in dibromomethane, bromochloromethane, and dichloromethane have been measured in the temperature range from 293.15 to 313.15 K and at pressures up to 100 MPa. Densities and isobaric heat capacities at atmospheric pressure have been also determined. Experimental results were used to calculate the densities and isobaric heat capacities as the function of temperature and pressure by means of a numerical integration technique. Moreover, experimental data at atmospheric pressure were then used to determine the SAFT-VR Mie molecular parameters for these liquids. The accuracy of the model has been then evaluated using a comparison of derived experimental high-pressure data with those predicted using SAFT. It was found that the model provide the possibility to predict also the isobaric heat capacity of all selected haloalkanes within an error up to 6%.

Cable correction of membrane currents recorded from root hairs of Arabidopsis thaliana L.

Membrane currents were recorded under voltage clamp from root hairs of Arabidopsis thaliana L. using the two-electrode method. Concurrent measurements of membrane voltage distal to the point of current injection were also carried out to assess the extent of current dissipation along the root hair axis. Estimates of the characteristic cable length, λ, showed this parameter to be a function both of membrane voltage and of substrate concentration for transport. The mean value for λ at 0 mV was 103 ± 20 μm (n=17), but ranged by as much as 6-fold in any one cell for membrane voltages from -300 to +40 mV and was affected by 0.25 to 3-fold at any one voltage on raising [K⁺]₀ from 0.1 to 10 mol m^-3. Current dissipation along the length of the cells lead to serious distortions of the current-voltage [I-V) characteristic, including consistent underestimates of membrane current as well as a general linearization of the I-V curve and a masking of conductance changes in the presence of transported substrates. In some experiments, microelectrodes were also placed in neighbouring epidermal cells to record the extent of intercellular coupling. Even with current-passing microelectrodes placed at the base of root hairs, coupling was ≤5% (voltage deflection of the epidermal cell ≤5% that recorded at the site of current injection), indicating an appreciable resistance to current passage between cells. These results demonstrate the feasibility of using root hairs as a 'single-cell model' in electrophysiological analyses of transport across the higher-plant plasma membrane; they also confirmed the need to correct for the cable properties of these cells on a cell-by-cell basis. © 1994 Oxford University Press.

A Schamel equation for ion acoustic waves in superthermal plasmas

An investigation of the propagation of ion acoustic waves in nonthermal plasmas in the presence of trapped electrons has been undertaken. This has been motivated by space and laboratory plasma observations of plasmas containing energetic particles, resulting in long-tailed distributions, in combination with trapped particles, whereby some of the plasma particles are confined to a finite region of phase space. An unmagnetized collisionless electron-ion plasma is considered, featuring a non-Maxwellian-trapped electron distribution, which is modelled by a kappa distribution function combined with a Schamel distribution. The effect of particle trapping has been considered, resulting in an expression for the electron density. Reductive perturbation theory has been used to construct a KdV-like Schamel equation, and examine its behaviour. The relevant configurational parameters in our study include the superthermality index κ and the characteristic trapping parameter β. A pulse-shaped family of solutions is proposed, also depending on the weak soliton speed increment u₀. The main modification due to an increase in particle trapping is an increase in the amplitude of solitary waves, yet leaving their spatial width practically unaffected. With enhanced superthermality, there is a decrease in both amplitude and width of solitary waves, for any given values of the trapping parameter and of the incremental soliton speed. Only positive polarity excitations were observed in our parametric investigation. 

K-Theory of non-linear projective toric varieties

We define a category of quasi-coherent sheaves of topological spaces on projective toric varieties and prove a splitting result for its algebraic K-theory, generalising earlier results for projective spaces. The splitting is expressed in terms of the number of interior lattice points of dilations of a polytope associated to the variety. The proof uses combinatorial and geometrical results on polytopal complexes. The same methods also give an elementary explicit calculation of the cohomology groups of a projective toric variety over any commutative ring.

R-matrix-Floquet theory of multiphoton processes:VIII. A linear equations method

A new linear equations method for calculating the R-matrix, which arises in the R-matrix-Floquet theory of multiphoton processes, is introduced. This method replaces the diagonalization of the Floquet Hamiltonian matrix by the solution of a set of linear simultaneous equations which are solved, in the present work, by the conjugate gradient method. This approach uses considerably less computer memory and can be readily ported onto parallel computers. It will thus enable much larger problems of current interest to be treated. This new method is tested by applying it to three-photon ionization of helium at frequencies where double resonances with a bound state and autoionizing states are important. Finally, an alternative linear equations method, which avoids the explicit calculation of the R-matrix by incorporating the boundary conditions directly, is described in an appendix.