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

We propose a memory form of exchange-correlation potential v_XC(r, t) for time-dependent interacting many-particle systems. Unlike previous memory-XC potentials, our v_XC is not limited to the linear response regime. The proposed form of v_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 v_XC based solely on an existing parametrization of the linear XC response kernel f^hom_XC(n, ω) of the uniform gas. Application to quantum wells seems promising.