Dynamic response function and bounds of the susceptibility of a semiclassical gas and Kramers-Kronig relations in optic-data inversion

The frequency-dependent density-density response function for a semiclassical gas has been calculated from its defining equation of linear-response theory. The particular form of the response function appears to be relevant to optic-data inversion using Kramers-Kronig relations. Also the zero-frequency limit of the response function, being the static susceptibility, is a bounded function. The susceptibility for the semiclassical gas model provides a unique opportunity to test the bounds analytically. This study further suggests a slightly different derivation of the lower bounds, perhaps less abstract than by convexity theory via Jensen's inequality.