Electrostatic interactions in host-guest complexes 2

In this article the quantum chemically calculated charge density distribution of 18-crown-6 and the K+ 18-crown-6 complex are compared with the charge density distribution of smaller molecules and corresponding complexes which can be considered as fragments of the 18-crown-6 molecule. An analysis of the charge density distribution in terms of atomic charge distribution according to the stockholder recipe gives accurate rules for the transferability of the charge density distribution. This gives us the possibility to construct the charge density distribution of large molecules out of accurate large basis set results on small molecules

The Statistics of Density Peaks and the Column Density Distribution of the Lyman-Alpha Forest

We develop a method to calculate the column density distribution of the Lyman-alpha forest for column densities in the range $10^{12.5} - 10^{14.5} cm^{-2}$. The Zel'dovich approximation, with appropriate smoothing, is used to compute the density and peculiar velocity fields. The effect of the latter on absorption profiles is discussed and it is shown to have little effect on the column density distribution. An approximation is introduced in which the column density distribution is related to a statistic of density peaks (involving its height and first and second derivatives along the line of sight) in real space. We show that the slope of the column density distribution is determined by the temperature-density relation as well as the power spectrum on scales $2 h Mpc^{-1} < k < 20 h Mpc^{-1}$. An expression relating the three is given. We find very good agreement between the column density distribution obtained by applying the Voigt-profile-fitting technique to the output of a full hydrodynamic simulation and that obtained using our approximate method for a test model. This formalism then is applied to study a group of CDM as well as CHDM models. We show that the amplitude of the column density distribution depends on the combination of parameters $(\Omega_b h^2)^2 T_0^{-0.7} J_{HI}^{-1}$, which is not well-constrained by independent observations. The slope of the distribution, on the other hand, can be used to distinguish between different models: those with a smaller amplitude and a steeper slope of the power spectrum on small scales give rise to steeper distributions, for the range of column densities we study. Comparison with high resolution Keck data is made.Comment: match accepted version; discussion added: the effect of the shape of the power spectrum on the slope of the column density distributio

A first step towards a direct inversion of the Lyman forest in QSO spectra

A method for the recovery of the real space line-of-sight mass density field from Lyman absorption in QSO spectra is presented. The method makes use of a Lucy-type algorithm for the recovery of the HI density. The matter density is inferred from the HI density assuming that the absorption is due to a photoionized intergalactic medium which traces the mass distribution as suggested by recent numerical simulations. Redshift distortions are corrected iteratively from a simultaneous estimate of the peculiar velocity. The method is tested with mock spectra obtained from N-body simulations. The density field is recovered reasonably well up to densities where the absorption features become strongly saturated. The method is an excellent tool to study the density probability distribution and clustering properties of the mass density in the (mildly) non-linear regime. Combined with redshift surveys along QSO sightlines the method will make it possible to relate the clustering of high-redshift galaxies to the clustering of the underlying mass density. We further show that accurate estimates for \Omega_{bar}h^2)^2 J^{-1} H(z)^{-1} and higher order moments of the density probability function can be obtained despite the missing high density tail of the density distribution if a parametric form for the probability distribution of the mass density is assumed.Comment: 10 pages, 6 figure

Probability distribution of the vacuum energy density

As the vacuum state of a quantum field is not an eigenstate of the Hamiltonian density, the vacuum energy density can be represented as a random variable. We present an analytical calculation of the probability distribution of the vacuum energy density for real and complex massless scalar fields in Minkowski space. The obtained probability distributions are broad and the vacuum expectation value of the Hamiltonian density is not fully representative of the vacuum energy density.Comment: 5 pages, 2 figures, revised version to appear in Phys.Rev.