A mathematical formulation of the random phase approximation for crystals

We study the response of crystals to an external, time-dependent forcing by considering the time evolution of localized defects. The aim of this work is to extend previous results on the static (time-independent) response of crystals. The linear response allows to define the frequency-dependent polarization operator. On the other hand, the nonlinear response allows to derive, in some spatial homogenization limit, the expression of the frequency-dependent permittivity of a crystal in terms of its band structure.

This is joint work with Eric Cances.