Nonlinear response I: General considerations

Abstract The linear response technique of Kubo is extended to treat the response of a system to quadratic order in the external field. Nonlinear equations of motion for a set of slowly varying macroscopic variables, a ( t ), are obtained. These equations express the time derivative of a ( t ) in terms of a ( t ) and a ( t ) a ( t ) and time-dependent coefficients which involve equilibrium correlation functions. The coefficient of a ( t ) is identical to that found from linear response theory. A discussion of the long-time behavior of the coefficients is presented.