Compact two-electron wave function for bond dissociation and Van der Waals interactions: A natural amplitude assessment

Electron correlations in molecules can be divided in short range dynamical correlations, long range Van der Waals type interactions and near degeneracy static correlations. In this work we analyze for a one-dimensional model of a two-electron system how these three types of correlations can be incorporated in a simple wave function of restricted functional form consisting of an orbital product multiplied by a single correlation function $f(r_{12})$ depending on the interelectronic distance $r_{12}$. Since the three types of correlations mentioned lead to different signatures in terms of the natural orbital (NO) amplitudes in two-electron systems we make an analysis of the wave function in terms of the NO amplitudes for a model system of a diatomic molecule. In our numerical implementation we fully optimize the orbitals and the correlation function on a spatial grid without restrictions on their functional form. Due to this particular form of the wave function, we can prove that none of the amplitudes vanishes and moreover that it displays a distinct sign pattern and a series of avoided crossings as a function of the bond distance in agreement with the exact solution. This shows that the wave function Ansatz correctly incorporates the long range Van der Waals interactions. We further show that the approximate wave function gives an excellent binding curve and is able to describe static correlations. We show that in order to do this the correlation function $f(r_{12})$ needs to diverge for large $r_{12}$ at large internuclear distances while for shorter bond distances it increases as a function of $r_{12}$ to a maximum value after which it decays exponentially. We further give a physical interpretation of this behavior.Comment: 16 pages, 13 figure

Tumbling of a rigid rod in a shear flow

The tumbling of a rigid rod in a shear flow is analyzed in the high viscosity limit. Following Burgers, the Master Equation is derived for the probability distribution of the orientation of the rod. The equation contains one dimensionless number, the Weissenberg number, which is the ratio of the shear rate and the orientational diffusion constant. The equation is solved for the stationary state distribution for arbitrary Weissenberg numbers, in particular for the limit of high Weissenberg numbers. The stationary state gives an interesting flow pattern for the orientation of the rod, showing the interplay between flow due to the driving shear force and diffusion due to the random thermal forces of the fluid. The average tumbling time and tumbling frequency are calculated as a function of the Weissenberg number. A simple cross-over function is proposed which covers the whole regime from small to large Weissenberg numbers.Comment: 22 pages, 9 figure

Free energies in the presence of electric and magnetic fields

We discuss different free energies for materials in static electric and magnetic fields. We explain what the corresponding Hamiltonians are, and describe which choice gives rise to which result for the free energy change, dF, in the thermodynamic identity. We also discuss which Hamiltonian is the most appropriate for calculations using statistical mechanics, as well as the relationship between the various free energies and the "Landau function", which has to be minimized to determine the equilibrium polarization or magnetization, and is central to Landau's theory of second order phase transitions

Many-body Green's function theory for electron-phonon interactions: ground state properties of the Holstein dimer

We study ground-state properties of a two-site, two-electron Holstein model describing two molecules coupled indirectly via electron-phonon interaction by using both exact diagonalization and self-consistent diagrammatic many-body perturbation theory. The Hartree and self-consistent Born approximations used in the present work are studied at different levels of self-consistency. The governing equations are shown to exhibit multiple solutions when the electron-phonon interaction is sufficiently strong whereas at smaller interactions only a single solution is found. The additional solutions at larger electron-phonon couplings correspond to symmetry-broken states with inhomogeneous electron densities. A comparison to exact results indicates that this symmetry breaking is strongly correlated with the formation of a bipolaron state in which the two electrons prefer to reside on the same molecule. The results further show that the Hartree and partially self-consistent Born solutions obtained by enforcing symmetry do not compare well with exact energetics, while the fully self-consistent Born approximation improves the qualitative and quantitative agreement with exact results in the same symmetric case. This together with a presented natural occupation number analysis supports the conclusion that the fully self-consistent approximation describes partially the bipolaron crossover. These results contribute to better understanding how these approximations cope with the strong localizing effect of the electron-phonon interaction.Comment: 9 figures, corrected typo

Strongly coupled modes in a weakly driven micromechanical resonator

We demonstrate strong coupling between the flexural vibration modes of a clamped-clamped micromechanical resonator vibrating at low amplitudes. This coupling enables the direct measurement of the frequency response via amplitude- and phase modulation schemes using the fundamental mode as a mechanical detector. In the linear regime, a frequency shift of $\mathrm{0.8\,Hz}$ is observed for a mode with a line width of $\mathrm{5.8\,Hz}$ in vacuum. The measured response is well-described by the analytical model based on the Euler-Bernoulli beam including tension. Calculations predict an upper limit for the room-temperature Q-factor of $\mathrm{4.5\times10^5}$ for our top-down fabricated micromechanical beam resonators.Comment: 9 pages, 2 figure

The photochemistry and photophysics of a series of alpha octa(alkyl-substituted) silicon, zinc and palladium phthalocyanines

Photophysical and photochemical measurements have been made on a series of novel alpha octa(alkyl-substituted) silicon, zinc and palladium phthalocyanines for which the synthesis is outlined. Fluorescence quantum yields and lifetimes, triplet quantum yields and lifetimes and singlet delta oxygen quantum yields were measured in 1% v/v pyridine in toluene. The effects of varying central atom and addition of alkyl substituents relative to unsubstituted parent molecules, zinc phthalocyanine (ZnPc) and silicon phthalocyanine (SiPc), are discussed. All phthalocyanines studied exhibit absorption and emission maxima in the region of 680–750 nm with molar absorptivity of the Q-band 105 M−1 cm−1. The series of compounds also exhibited triplet quantum yields of 0.65–0.95 and singlet oxygen quantum yields of 0.49–0.93

Intermittent nulls in PSR B0818-13, and the subpulse-drift alias mode

We show that all long nulls in PSR B0818-13 are trains of rapidly alternating nulls and pulses (each shorter than one pulse period). Sometimes only the nulls coincide with our pulse window, resulting in one of the apparently long nulls seen occasionally. We show these are seen as often as expected if during such a train the probability for nulls is 1.2 times less than for pulses. During nulls, the subpulse drift-speed appears to increase. We assume that the carousel of sparks that possibly underlies the subpulses actually slows down, as it does in similar pulsars like PSR B0809+74, and conclude that the subpulse-drift in this pulsar must be aliased. The carousel must then rotate in 30 seconds or less, making it the fastest found to date.Comment: Accepted for A&A. 7 pages with low-resolution images; high-resolution versions are available at http://www.astro.uu.nl/~jleeuwen/preprints/0818-nulls

Measuring the impact of observations on the predictability of the Kuroshio Extension in a shallow-water model

In this paper sequential importance sampling is used to assess the impact of observations on a ensemble prediction for the decadal path transitions of the Kuroshio Extension (KE). This particle filtering approach gives access to the probability density of the state vector, which allows us to determine the predictive power — an entropy based measure — of the ensemble prediction. The proposed set-up makes use of an ensemble that, at each time, samples the climatological probability distribution. Then, in a post-processing step, the impact of different sets of observations is measured by the increase in predictive power of the ensemble over the climatological signal during one-year. The method is applied in an identical-twin experiment for the Kuroshio Extension using a reduced-gravity shallow water model. We investigate the impact of assimilating velocity observations from different locations during the elongated and the contracted meandering state of the KE. Optimal observations location correspond to regions with strong potential vorticity gradients. For the elongated state the optimal location is in the first meander of the KE. During the contracted state of the KE it is located south of Japan, where the Kuroshio separates from the coast

Numerical simulations on the motion of atoms travelling through a standing-wave light field

The motion of metastable helium atoms travelling through a standing light wave is investigated with a semi-classical numerical model. The results of a calculation including the velocity dependence of the dipole force are compared with those of the commonly used approach, which assumes a conservative dipole force. The comparison is made for two atom guiding regimes that can be used for the production of nanostructure arrays; a low power regime, where the atoms are focused in a standing wave by the dipole force, and a higher power regime, in which the atoms channel along the potential minima of the light field. In the low power regime the differences between the two models are negligible and both models show that, for lithography purposes, pattern widths of 150 nm can be achieved. In the high power channelling regime the conservative force model, predicting 100 nm features, is shown to break down. The model that incorporates velocity dependence, resulting in a structure size of 40 nm, remains valid, as demonstrated by a comparison with quantum Monte-Carlo wavefunction calculations.Comment: 9 pages, 4 figure