Theory of quadratic response functions

Abstract

The general quantum theory of quadratic response functions, such as the optical-frequency quadratic polarizability of dielectrics, is developed on the lines of Kubo's density matrix-Green's function theory of linear response functions. Sum rule series are obtained, and applied to the quadratic polarizability. A suitable form of Kramers-Kronig relations for quadratic response functions is developed. © 1963 The American Physical Society.