The Dielectric Constant and the Conductivity of an Electrolyte Solution at Finite Wave-Lengths and Frequencies

We derive expressions for the dielectric constant and the conductivity of an electrolyte solution at finite wave-lengths and frequencies in terms of the correlation functions of the electrical current and the polarization. These relationships depend on the geometry of the system and two particular cases are considered in detail: the infinite system and systems with periodic boundary conditions which are commonly used in molecular-dynamics simulations. In addition, in the latter case, the so-called perfect screening condition is expressed in a way that permits the computation of the equilibrium dielectric constant in a simulation.