Thesis (doctoral)--Göteborg University, 2008. / Includes bibliographical references.

A new approach is developed for evaluating the mixing properties of binary solutions at high pressure. This involves solving Poisson's equation throughout three-dimensional cubic lattices, consistent with Thomas-Fermi-Dirac (TFD) theory. Zero temperature calculations are carried out for a variety of compositions and crystal structures in 3 pressure groups relevant to Jovian planetary interiors. Pseudopotentials based on the two-component-plasma model (with a uniform electron background) are fitted to the solid-state results, and are then used in liquid-state calculations using hard-sphere perturbation theory. TFD results for H-He solutions find critical temperatures (above which all compositions are soluble) to be ∿ 0, 500, and 1500°K at pressures of 10, 100, and 1000 Mbar, respectively. These temperatures are much lower than those obtained using free electron perturbation theory, where T(crit) ∿ 10,000°K at 10 Mbar. Thus, unlike the perturbation theory results, the TFD results predict that helium should be soluble in metallic hydrogen in the deep interiors of both Jupiter and Saturn, and our calculations give an indication of the degree of model-dependence in computing high pressure mixing properties. In addition, TFD calculations for H-C and H-O solutions find phase separation temperatures to be≲ 10⁴ °K for pressures ≲ 10³ Mbar. These temperatures are considerably lower than those found assuming a uniform electron distribution (where T(crit) ≳ 10⁵ °K), and suggest that H-C and H-O solutions should also be miscible in the metallic zones of Jupiter and Saturn.

Thesis (Ph. D.)--University of Texas at Austin, 2008. / Vita. Includes bibliographical references.

The two-dimensional electronic systems (2DESs) have kept surprising physicists for the last few decades. Examples include the integer and fractional quantum Hall effects, cuprate superconductivity, and graphene. This thesis is intended to develop suitable theoretical tools which can be generalized to study new types of 2DESs with strong correlation feature. The first part of this thesis describes the investigation of heterostructures made by Mott insulators. This work is mostly motivated by the significant improvement of techniques for layer-by-layer growth of transition metal oxides in the last few years. We construct a toy model based on generalized Hubbard model complemented with long-ranged Coulomb interaction, and we study it by Hartree-Fock theory, dynamical mean-field theory, and Thomas-Fermi theory. We argue that interesting 2D strongly correlated electronic systems can be created in such heterostructures under several conditions. Since these 2D systems are formed entirely due to the gap generated by electron-electron interaction, they are not addiabatically connected to a noninteracting electron states. This feature makes these 2D systems distinguish from the ones created in semiconductor heterostructures, and they may be potential systems having non-Fermi liquid behaviors. The second part of this thesis is devoted to the study of collective excitations in high-temperature superconductors. One important achievement in this work is to develop a time-dependent mean-field theory for t-U-J-V model, an effective low energy model for cuprates. The time-dependent mean-field theory is proven to be identical to the generalized random-phase approximation (GRPA) which includes both the bubble and ladder diagrams. We propose that the famous 41 meV magnetic resonance mode observed in the inelastic neutron scattering measurements is a collective mode arising from a conjugation relation, which has been overlooked in previous work, between the antiferromagnetic fluctuation and the phase fluctuation of the d-wave superconducting order parameter near momentum ([pi, pi]). Furthermore, we find that this collective mode signals the strength of the antiferromagnetic fluctuations which are responsible for the suppression of the superfluid density in the underdoped cuprates even at zero temperature. Finally, we perform a complete analysis on an effective model with parameters fitted by experimental data of Bi2212 within the GRPA scheme and conclude that the short-range antiferromagnetic interactions which are a remnant of the parent Mott-insulator are more likely the pairing mechanism of the High-T[subscript c] cuprates. / text