The random-phase approximation (RPA) as an approach for computing the electronic correlation energy is reviewed. After a brief account of its basic concept and historical development, the paper is devoted to the theoretical formulations of RPA, and its applications to realistic systems. With several illustrating applications, we discuss the implications of RPA for computational chemistry and materials science. The computational cost of RPA is also addressed which is critical for its widespread use in future applications. In addition, current correction schemes going beyond RPA and directions of further development will be discussed.

Using a two-dimensional Hubbard Hamiltonian for the three electronic bands crossing the Fermi level in Sr2RuO4 we calculate the band structure and spin susceptibility χ(q, ω) in quantitative agreement with nuclear magnetic resonance (NMR) and inelastic neutron scattering (INS) experiments. The susceptibility has two peaks at Qi = (2π/3, 2π/3) due to the nesting Fermi surface properties and at qi = (0.6π, 0) due to the tendency towards ferromagnetism. Applying spin-fluctuation exchange theory as in layered cuprates we determine from χ(q, ω), electronic dispersions, and Fermi surface topology that superconductivity in Sr2RuO4 consists of triplet pairing. Combining the Fermi surface topology and the results for χ(q, ω) we can exclude s− and d−wave symmetry for the superconducting order parameter. Furthermore, within our analysis and approximations we find that f -wave symmetry is slightly favored over p-wave symmetry due to the nesting properties of the Fermi surface. 74.20.Mn, 74.25.Ha

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Motivated by a recent experiment, we study the microwave-induced photoconductivity of a twodimensional electron gas arising from intra-Landau-level transitions within a model where the electrons are subject to a unidirectional periodic potential in addition to a weaker impurity potential. With appropriate identifications, our results can be compared to experiment and allow us to explain the sign of the photocurrent, its dependence on magnetic field and microwave frequency as well as the microwave-induced suppression of the Shubnikov-deHaas oscillations.

In an attempt to characterize the distribution of forms and shapes of nodal domains in wave functions, we define a geometric parameter -the ratio ρ between the area of a domain and its perimeter, measured in units of the wavelength 1/ √ E. We show that the distribution function P (ρ) can distinguish between domains in which the classical dynamics is regular or chaotic. For separable surfaces, we compute the limiting distribution, and show that it is supported by an interval, which is independent of the properties of the surface. In systems which are chaotic, or in random-waves, the area-to-perimeter distribution has substantially different features which we study numerically. We compare the features of the distribution for chaotic wave functions with the predictions of the percolation model to find agreement, but only for nodal domains which are big with respect to the wavelength scale. This work is also closely related to, and provides a new point of view on isoperimetric inequalities.