Dynamical correlation in electron liquids

Several aspects of dynamical correlation in electron liquids are considered.; First, the dynamic response of an interacting electron system in d-dimensions is determined by an extension of the relaxation-time approximation forced to obey local conservation laws for number, momentum and energy. A consequence of these imposed constraints is that the local electron equilibrium distribution must have a space- and time-dependent chemical potential, drift velocity and temperature. The consequences for a hydrodynamic theory are considered, and by incorporating the competition between relaxation and inertial effects we derive generalized hydrodynamic equations applicable to arbitrary frequencies.; Secondly, spin correlations in an electron liquid are studied in the high-frequency limit. The third-moment sum rule is evaluated and then used to derive exact limiting forms (at both long- and short-wavelengths) for the spin-antisymmetric local-field factor, G_ (q, ∞). In two dimensions G_ (q, ∞) is found to diverge as 1/q at long wavelengths, and the spin-antisymmetric exchange-correlation kernel of time-dependent spin density functional theory diverges as 1/q2 in both two and three dimensions, signalling a failure of the local-density approximation.; Thirdly, we present an analytical study of all the local-field factors in a homogeneous, isotropic, two-dimensional electron liquid as a function of all momentum, imaginary frequency, and density. New sum rules are derived which constrain both the spin-symmetric and spin-antisymmetric response functions. Parameterized expressions for the local-field factors are proposed, based on both sum rules and many-body perturbation theory, and are found to be in good agreement with Quantum Monte Carlo calculations. These expressions are used to evaluate the effective electron-electron interaction via the modified Kukkonen-Overhauser approximation.; Finally, the modified Kukkonen-Overhauser effective electron-electron interaction is used to numerically solve the Eliashberg equation to investigate the possibility of intrinsic electron pairing in isotropic two-dimensional systems. Intrinsic p-wave and d-wave pairing is found for the one-band case at r_s values of 2, 5, and 10. Two-band systems also exhibit s-wave pairing solutions at r_s values of 5 and 10.