Hydrodynamic theory for quantum plasmonics: Linear-response dynamics of the inhomogeneous electron gas

We investigate the hydrodynamic theory of metals, offering systematic studies of the linear-response dynamics for an inhomogeneous electron gas. We include the quantum functional terms of the Thomas-Fermi kinetic energy, the von Weizs\"acker kinetic energy, and the exchange-correlation Coulomb energies under the local density approximation. The advantages, limitations, and possible improvements of the hydrodynamic theory are transparently demonstrated. The roles of various parameters in the theory are identified. We anticipate that the hydrodynamic theory can be applied to investigate the linear response of complex metallic nanostructures, including quantum effects, by adjusting theory parameters appropriately.