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The time-dependent density functional (TDDFT) equations may be written eitherfor the Kohn-Sham orbitals in Hilbert space or for the single electron densitymatrix in Liouville space. A collective-oscillator, quasiparticle,representation of the density response of many-electron systems whichexplicitly reveals the relevant electronic coherence sizes is developed usingthe Liouville space representation of adiabatic TDDFT. Closed expressions forthe nonlinear density-density response are derived, eliminating the need tosolve nonlinear integral equations, as required in the Hilbert spaceformulation of the response.Comment: 24 page

Quasiparticle density-matrix representation of nonlinear time-dependent density-functional response functions