In defense of the "tunneling" wave function of the universe

The tunneling approach to the wave function of the Universe has been recently criticized by Bousso and Hawking who claim that it predicts a catastrophic instability of de Sitter space with respect to pair production of black holes. We show that this claim is unfounded. First, we argue that different horizon size regions in de Sitter space cannot be treated as independently created, as they contend. And second, the WKB tunneling wave function is not simply the inverse of the Hartle-Hawking one, except in very special cases. Applied to the related problem of pair production of massive particles, we argue that the tunneling wave function leads to a small constant production rate, and not to a catastrophe as the argument of Bousso and Hawking would suggest.

Linear response functions for a vibrational configuration interaction state

Linear response functions are implemented for a vibrational configuration interaction state allowing accurate analytical calculations of pure vibrational contributions to dynamical polarizabilities. Sample calculations are presented for the pure vibrational contributions to the polarizabilities of water and formaldehyde. We discuss the convergence of the results with respect to various details of the vibrational wave function description as well as the potential and property surfaces. We also analyze the frequency dependence of the linear response function and the effect of accounting phenomenologically for the finite lifetime of the excited vibrational states. Finally, we compare the analytical response approach to a sum-over-states approach

Effective atomic orbitals for fuzzy atoms

The method of extracting effective atomic orbitals and effective minimal basis sets from molecular wave function characterizing the state of an atom in a molecule is developed in the framework of the "fuzzy" atoms. In all cases studied, there were as many effective orbitals that have considerable occupation numbers as orbitals in the classical minimal basis. That is considered to be of high conceptual importance

Nonmesonic weak decay of the hypertriton

The nonmesonic decay of the hypertriton is calculated based on a hypertriton wave function and 3N scattering states, which are rigorous solutions of three-body Faddeev equations using realistic NN and hyperon-nucleon interactions. The pion exchange together with heavier meson exchanges for the ¿N¿NN transition is considered. The total nonmesonic decay rate is found to be 0.5% of the free ¿ decay rate. Integrated as well as differential decay rates are given. The p- and n-induced decays are discussed thoroughly and it is shown that the corresponding total rates cannot be measured individually.

Delta(1232) isobar excitations in nuclear many-body systems from varios NN interactions.

Delta isobar components in the nuclear many-body wave function are investigated for the deuteron, light nuclei (16O), and infinite nuclear matter within the framework of the coupled-cluster theory. The predictions derived for various realistic models of the baryon-baryon interaction are compared to each other. These include local (V28) and nonlocal meson exchange potentials (Bonn2000) but also a model recently derived by the Salamanca group accounting for quark degrees of freedom. The characteristic differences which are obtained for the NDelta and Delta Delta correlation functions are related to the approximation made in deriving the matrix elements for the baryon-baryon interaction.

Ground-state properties of a dilute homogeneous Bose gas of hard disks in two dimensions

The energy and structure of a dilute hard-disks Bose gas are studied in the framework of a variational many-body approach based on a Jastrow correlated ground-state wave function. The asymptotic behaviors of the radial distribution function and the one-body density matrix are analyzed after solving the Euler equation obtained by a free minimization of the hypernetted chain energy functional. Our results show important deviations from those of the available low density expansions, already at gas parameter values x~0.001 . The condensate fraction in 2D is also computed and found generally lower than the 3D one at the same x.

Symmetry breaking in small rotating clouds of trapped ultracold Bose atoms

We study the signatures of rotational and phase symmetry breaking in small rotating clouds of trapped ultracold Bose atoms by looking at rigorously defined condensate wave function. Rotational symmetry breaking occurs in narrow frequency windows, where energy degeneracy between the lowest energy states of different total angular momentum takes place. This leads to a complex condensate wave function that exhibits vortices clearly seen as holes in the density, as well as characteristic local phase patterns, reflecting the appearance of vorticities. Phase symmetry (or gauge symmetry) breaking, on the other hand, is clearly manifested in the interference of two independent rotating clouds.

Boson-boson mixtures and triplet correlations

The hypernetted-chain formalism for boson-boson mixtures described by an extended Jastrow correlated wave function is derived, taking into account elementary diagrams and triplet correlations. The energy of an ideal boson 3He-4He mixture is computed for low values of the 3He concentration. The zero-3He-concentration limit provides a 3He chemical potential in good agreement with the experimental value, when a McMillan two-body correlation factor and the Lennard-Jones potential are adopted. If the Euler equations for the two-body correlation factors are solved in presence of triplet correlations, the agreement is again improved. At the experimental 4He equilibrium density, the 3He chemical potential turns out to be -2.58 K, to be compared with the experimental value, -2.79 K.

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.

Variational study of 3He-4He mixtures

The ground-state properties of the 3He-4He mixture are investigated by assuming the wave function to be a product of pair correlations. The antisymmetry of the 3He component is taken into account by Fermi-hypernetted-chain techniques and the results are compared with those obtained from the lowest-order Wu-Feenberg expansion and the boson-boson approximation. A little improvement is found in the 3He maximum solubility. A microscopic theory to calculate 3He static properties such as zero-concentration chemical potential and excess-volume parameter is derived and the results are compared with the experiments.

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.

Resonating-valence-bond theory for the square-planar lattice

The short-range resonating-valence-bond (RVB) wave function with nearest-neighbor (NN) spin pairings only is investigated as a possible description for the Heisenberg model on a square-planar lattice. A type of long-range order associated to this RVB Ansatz is identified along with some qualitative consequences involving lattice distortions, excitations, and their coupling.

Evidence for two different bonding mechanisms of Al on Si(111)

By means of the ab initio cluster-model approach, we present theoretical evidence for two different mechanisms of bonding of atomic Al to Si(111). On the atop site (T1) the interaction of atomic Al to Si(111) is characteristic of an ionic bond whereas interaction above the threefold eclipsed site (T4) leads to the formation of a typical covalent bond. Moreover, both sites have a similar interaction energy if electronic correlation effects are included. While the conclusions regarding the nature of the chemisorption bond in the two sites do not depend either on the cluster-model size, the kind of embedding hydrogen atoms used, or the quality of the wave function (Hartree-Fock or configuration interaction), the chemisorption energy depends strongly on the wave function used. In fact, inclusion of correlation energy is necessary to properly describe the interaction energies.

Ab initio valence-bond cluster model for ionic solids: Alkaline-earth oxides

A linear M-O-M (M=metal, O=oxygen) cluster embedded in a Madelung field, and also including the quantum effects of the neighboring ions, is used to represent the alkaline-earth oxides. For this model an ab initio wave function is constructed as a linear combination of Slater determinants written in an atomic orbital basis set, i.e., a valence-bond wave function. Each valence-bond determinant (or group of determinants) corresponds to a resonating valence-bond structure. We have obtained ab initio valence-bond cluster-model wave functions for the electronic ground state and the excited states involved in the optical-gap transitions. Numerical results are reasonably close to the experimental values. Moreover, the model contains the ionic model as a limiting case and can be readily extended and improved.

Extent and limitations of density functional theory in describing magnetic systems

The performance of density-functional theory to solve the exact, nonrelativistic, many-electron problem for magnetic systems has been explored in a new implementation imposing space and spin symmetry constraints, as in ab initio wave function theory. Calculations on selected systems representative of organic diradicals, molecular magnets and antiferromagnetic solids carried out with and without these constraints lead to contradictory results, which provide numerical illustration on this usually obviated problem. It is concluded that the present exchange-correlation functionals provide reasonable numerical results although for the wrong physical reasons, thus evidencing the need for continued search for more accurate expressions.