Anomalous behavior of plasma response functions at strong coupling

Using data from equilibrium Molecular Dynamics computer simulations we have built up a catalogue of response functions for the Coulomb one-component plasma (OCP) over a wide range of $\Gamma$ coupling values, including the strongly coupled $\Gamma > 1$ liquid regime. We focus on the domain of negative compressibility ($\Gamma>3$), where causality and the concomitant Kramers-Kronig relations are violated. We give a description of the details of the violation, both in the frequency and time domains. We show that the viscoelastic pole of the density response function morphs into an imaginary pole in the upper $\omega$ half-plane that is responsible for the anomalous behavior of the response in this coupling range. By examining the plasmon dispersion relation through the dielectric response function, rather than via the peaks of the dynamical structure function, we obtain a more reliable representation for the dispersion. We demonstrate that there is an intimate link between the formation of the roton minimum in the dispersion and the negative compressibility of the system. The feasibility of the extension of our analysis to systems with a short range interaction is explored.