Nonlinear Response for Time-Dependent External Fields: Shear Flow and Color Conductivity

We present a generalization of the nonlinear response theory for autonomous systems which can be applied to classical many-body systems in large timedependent external fields. Our formalism represents the first practical application of response theory to such problems, and provides a method of evaluating averages of phase functions that is more efficient than direct computer simulation. Our expressions for the nonlinear time-dependent response are tested against nonequilibrium molecular dynamics computer simulation of two simple nonautonomous systems. The relation of our results to known special cases (time-dependent linear response and time-independent nonlinear response) is discussed.