Time-dependent density-matrix functional theory formalism to study biexcitonic phenomena in bulk systems and nanostructures*

We formulate a time-dependent density-matrix functional theory (TDDMFT) approach to study higher-order correlation effects like biexcitons in different bulk systems and nanostructures. In particular, we derive the TDDMFT version of the Schroedinger equation for biexcitons in terms of the one-body and two-body reduced density matrices. To test the approach, we calculate the biexcitonic binding energies in the case of different exchange- correlation (XC) potentials for bulk CuCl, CuBr, CdS and ZnO materials with rather large biexcitonic binding energies. We show that the excitonic, biexcitonic and other higher-order correlation effects are more pronounced in the case when the XC kernel contains a $1/q^{2}$ Coulomb singularity. Also, we analyze the role of non-adiabaticity of the XC potential in description of the higher-order correlation effects within the TDDMFT.