Scaling calculation of isoscalar giant resonances in relativistic Thomas-Fermi theory

We derive analytical expressions for the excitation energy of the isoscalar giant monopole and quadrupole resonances in finite nuclei, by using the scaling method and the extended ThomasFermi approach to relativistic mean-field theory. We study the ability of several nonlinear σω parameter sets of common use in reproducing the experimental data. For monopole oscillations the calculations agree better with experiment when the nuclear matter incompressibility of the relativistic interaction lies in the range 220260 MeV. The breathing-mode energies of the scaling method compare satisfactorily with those obtained in relativistic RPA and time-dependent mean-field calculations. For quadrupole oscillations, all the analyzed nonlinear parameter sets reproduce the empirical trends reasonably well.

Theory for correlation functions of processes driven by external colored noise

We study steady-state correlation functions of nonlinear stochastic processes driven by external colored noise. We present a methodology that provides explicit expressions of correlation functions approximating simultaneously short- and long-time regimes. The non-Markov nature is reduced to an effective Markovian formulation, and the nonlinearities are treated systematically by means of double expansions in high and low frequencies. We also derive some exact expressions for the coefficients of these expansions for arbitrary noise by means of a generalization of projection-operator techniques.

Density matrices and momentum distributions in 3He-4He mixtures

We report variational calculations, in the hypernetted-chain (HNC)-Fermi-HNC scheme, of one-body density matrices and one-particle momentum distributions for 3He-4He mixtures described by a Jastrow correlated wave function. The 4He condensate fractions and the 3He strength poles are examined and compared with the Monte Carlo available results. The agreement has been found to be very satisfactory. Their density dependence is also studied.

Microscopic calculations of the excitation spectrum of one 3He impurity in liquid 4He

We calculate the chemical potential ¿0 and the effective mass m*/m3 of one 3He impurity in liquid 4He. First a variational wave function including two- and three-particle dynamical correlations is adopted. Triplet correlations bring the computed values of ¿0 very close to the experimental results. The variational estimate of m*/m3 includes also backflow correlations between the 3He atom and the particles in the medium. Different approximations for the three-particle distribution function give almost the same values for m*/m3. The variational approach underestimates m*/m3 by ~10% at all of the considered densities. Correlated-basis perturbation theory is then used to improve the wave function to include backflow around the particles of the medium. The perturbative series built up with one-phonon states only is summed up to infinite order and gives results very close to the variational ones. All the perturbative diagrams with two independent phonons have then been summed to compute m*/m3. Their contribution depends to some extent on the form used for the three-particle distribution function. When the scaling approximation is adopted, a reasonable agreement with the experimental results is achieved.

Building predictive models of soil particle-size distribution

Is it possible to build predictive models (PMs) of soil particle-size distribution (psd) in a region with complex geology and a young and unstable land-surface? The main objective of this study was to answer this question. A set of 339 soil samples from a small slope catchment in Southern Brazil was used to build PMs of psd in the surface soil layer. Multiple linear regression models were constructed using terrain attributes (elevation, slope, catchment area, convergence index, and topographic wetness index). The PMs explained more than half of the data variance. This performance is similar to (or even better than) that of the conventional soil mapping approach. For some size fractions, the PM performance can reach 70 %. Largest uncertainties were observed in geologically more complex areas. Therefore, significant improvements in the predictions can only be achieved if accurate geological data is made available. Meanwhile, PMs built on terrain attributes are efficient in predicting the particle-size distribution (psd) of soils in regions of complex geology.

Processes models, environmental analyses, and cognitive architectures: Quo vadis quantum probability theory? (Commentary on Pothos and Busemeyer)

A lot of research in cognition and decision making suffers from a lack of formalism. The quantum probability program could help to improve this situation, but we wonder whether it would provide even more added value if its presumed focus on outcome models were complemented by process models that are, ideally, informed by ecological analyses and integrated into cognitive architectures.

Particle agglomeration study in rf silane plasmas: In situ study by polarization-sensitive laser light scattering

To determine self‐consistently the time evolution of particle size and their number density in situ multi‐angle polarization‐sensitive laser light scattering was used. Cross‐polarization intensities (incident and scattered light intensities with opposite polarization) measured at 135° and ex situ transmission electronic microscopy analysis demonstrate the existence of nonspherical agglomerates during the early phase of agglomeration. Later in the particle time development both techniques reveal spherical particles again. The presence of strong cross‐polarization intensities is accompanied by low‐frequency instabilities detected on the scattered light intensities and plasma emission. It is found that the particle radius and particle number density during the agglomeration phase can be well described by the Brownian free molecule coagulation model. Application of this neutral particle coagulation model is justified by calculation of the particle charge whereby it is shown that particles of a few tens of nanometer can be considered as neutral under our experimental conditions. The measured particle dispersion can be well described by a Brownian free molecule coagulation model including a log‐normal particle size distribution.

Diffraction theory of Fresnel lenses encoded in low-resolution devices

A mathematical model that describes the behavior of low-resolution Fresnel lenses encoded in any low-resolution device (e.g., a spatial light modulator) is developed. The effects of low-resolution codification, such the appearance of new secondary lenses, are studied for a general case. General expressions for the phase of these lenses are developed, showing that each lens behaves as if it were encoded through all pixels of the low-resolution device. Simple expressions for the light distribution in the focal plane and its dependence on the encoded focal length are developed and commented on in detail. For a given codification device an optimum focal length is found for best lens performance. An optimization method for codification of a single lens with a short focal length is proposed.

Diffraction theory of optimized low-resolution Fresnel encoded lenses

A mathematical model describing the behavior of low-resolution Fresnel encoded lenses (LRFEL's) encoded in any low-resolution device (e.g., a spatial light modulator) has recently been developed. From this model, an LRFEL with a short focal length was optimized by our imposing the maximum intensity of light onto the optical axis. With this model, analytical expressions for the light-amplitude distribution, the diffraction efficiency, and the frequency response of the optimized LRFEL's are derived.

Noise induced transitions in semiclassical cosmology

A semiclassical cosmological model is considered which consists of a closed Friedmann-Robertson-Walker spacetime in the presence of a cosmological constant, which mimics the effect of an inflaton field, and a massless, non-conformally coupled quantum scalar field. We show that the back-reaction of the quantum field, which consists basically of a nonlocal term due to gravitational particle creation and a noise term induced by the quantum fluctuations of the field, are able to drive the cosmological scale factor over the barrier of the classical potential so that if the universe starts near a zero scale factor (initial singularity), it can make the transition to an exponentially expanding de Sitter phase. We compute the probability of this transition and it turns out to be comparable with the probability that the universe tunnels from ``nothing'' into an inflationary stage in quantum cosmology. This suggests that in the presence of matter fields the back-reaction on the spacetime should not be neglected in quantum cosmology.

Vacuum decay in quantum field theory

We study the contribution to vacuum decay in field theory due to the interaction between the long- and short-wavelength modes of the field. The field model considered consists of a scalar field of mass M with a cubic term in the potential. The dynamics of the long-wavelength modes becomes diffusive in this interaction. The diffusive behavior is described by the reduced Wigner function that characterizes the state of the long-wavelength modes. This function is obtained from the whole Wigner function by integration of the degrees of freedom of the short-wavelength modes. The dynamical equation for the reduced Wigner function becomes a kind of Fokker-Planck equation which is solved with suitable boundary conditions enforcing an initial metastable vacuum state trapped in the potential well. As a result a finite activation rate is found, even at zero temperature, for the formation of true vacuum bubbles of size M-1. This effect makes a substantial contribution to the total decay rate.

Perturbations on domain walls and strings: A covariant theory

A covariant formalism is developed for describing perturbations on vacuum domain walls and strings. The treatment applies to arbitrary domain walls in (N+1)-dimensional flat spacetime, including the case of bubbles of a true vacuum nucleating in a false vacuum. Straight strings and planar walls in de Sitter space, as well as closed strings and walls nucleating during inflation, are also considered. Perturbations are represented by a scalar field defined on the unperturbed wall or string world sheet. In a number of interesting cases, this field has a tachyonic mass and a nonminimal coupling to the world-sheet curvature.