Accurate Continuum Theories For Condensed Matter Systems
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This dissertation presents the construction and application of novel accurate continuum theories to various many-body problems in condensed matter systems. We begin with the construction of a new "classical" density-functional theory for general molecular liquids which is based on an exact evaluation of the free energy of a noninteracting molecular gas. By adding terms which capture intermolecular interactions, we arrive at a theory which reproduces both the linear and nonlinear dielectric response of the liquid, the experimental correlation functions of the uniform phase and various thermodynamic properties, such as the surface tension or liquid-vapor coexistence. We then apply our "classical" density-functional theory to the liquid of greatest importance, water. We introduce new computational techniques for efficient evaluation of the free energy of noninteracting water molecules and apply the resulting theory to the study of liquid water at solid surfaces. In strong electric fields, we observe dielectric saturation in good agreement with previously published molecular dynamics calculations. Next, we introduce a new, joint time-dependent density-functional theory for the description of dissolved electronic systems in time-dependent external potentials. Starting from the exact action functional for electrons and nuclei of both the solute and the solvent, we systematically eliminate solvent degrees of freedom and finally arrive at a coarse-grained action functional which retains the detailed ab initio description only for the solute electrons while treating the solvent with an approximate continuum theory. We apply this theory to study electronic excitations of formaldehyde in aqueous solution and find good agreement between our predictions and experimental findings. Finally, we examine phonon-phonon interactions in carbon nanotubes using an elastic continuum theory with elastic constants obtained from ab initio calculations. The resulting theory allows us to predict intrinsic quality factors of the fundamental flexural mode for tubes of different lengths and radii, but also for different temperatures and strains. We find that the intrinsic quality factor at room temperature is about one order of magnitude higher than current experimental findings, indicating that there remains room for improvement in current devices. We also explore the possibility of carbon nanotube mass sensors with single yoctogram precision.