Formal Theory of Nonlinear Response

This paper presents the derivation of formal, exact expressions for "generalized response coefficients," quantities which characterize the response of a system to conservative forces of arbitrary strength and time dependence. The development avoids all expansions of the response in powers of the driving forces. The generalized response coefficients thus provide the basis for calculations of nonlinear effects in those situations for which expansions in powers of the forces are not suitable. It is shown how the linear and higher-order response functions obtained first by Kubo can be obtained in a relatively more compact way. The expressions corresponding to static forces are considered in some detail. Generalized response coefficients are also derived for systems in equilibrium; the lowest order of these is just the isothermal susceptibility as usually defined.