Time-Dependent Density Functional Theory beyond Linear Response: An Exchange-Correlation Potential with Memory

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