Nonlinear response a general perturbative treatment

A formal theory of the nonlinear response is given using the Volterra expansion of the effect in terms of the external driving cause. The related functional derivatives are interpreted as generalized transfer functions. This approach includes different perturbative expansions such as those used for instance in circuit analysis and quantum mechanics (Green's function method). In particular the time-ordered Kubo's formula is deduced. This treatment can also describe nonstationary processes and naturally takes into account spatial dispersion. As an example of the applicability of the method, a generalized Klein-Gordon model equation is considered, the role of spatial dispersion discussed, and a hierarchy of nonlocal transfer functions obtained. The expression of nonlinear susceptibilities in terms of linear susceptibility allows an extension of Miller's rule to orders higher than the second order and to nonlocal problems as well