Time-dependent density-matrix functional in Liouville space and the optical response of many-electron systems

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Abstract
A time-dependent functional approach is developed for calculating the dynamical optical response and ground-state properties of nonrelativistic fermion systems. The functional (effective action) uses the particle-hole components of the reduced single-electron density matrix as variables and is constructed using the natural orbitals as a reference. It is defined on pairs of trajectories that constitute a Liouville space path in the phase space of the classical analog of the quantum system. A perturbative ‘‘semiclassical’’ calculation of the effective Liouville-space action is used to incorporate correlation effects in the linear optical response.