Conservation sum rules for the quadratic density response function.

Abstract

The quadratic density response function has been shown to be determined by the three-point density correlations at equilibrium. Consequently, the conservation laws enjoyed by the density fluctuation are expected to have their manifestations in the quadratic density response function. New frequency-moment sum rules are established along these lines. We show that the lowest-order quadratic response function exhausts the quadratic equivalent of the f-sum rule.