Time-dependent density functional theory beyond linear response: An exchange-correlation potential with memory

We propose a memory form of exchange-correlation potential nu(XC)(r, t) for time-dependent interacting many-particle systems. Unlike previous memory-XC potentials, our nu(XC) is not limited to the linear response regime. The proposed form of nu(XC) is a generalized local-density approximation chosen so as to satisfy the nonlinear harmonic potential theorem and Newton's third law. For the case of the inhomogeneous electron gas, we give an explicit prescription for nu(XC) based solely on an existing parametrization of the linear XC response kernel f(XC)(hom)(n, omega) of the uniform gas. Application to quantum wells seems promising.