Polarizability tensor and Kramers-Heisenberg induction

A general expression for the semiclassical, nonrelativistic linear polarizability of an arbitrary volume element V has been derived in the long wavelength approximation. The derivation starts from the expectation value of the dipole strength, as in the original Kramers-Heisenberg paper about optical scattering by atoms. The main requirements underlying the present approach are a separate non-Hermitian part of the Hamiltonian and a frequency dependent damping, which is zero for the static case. Resonant and antiresonant exponentials are both found to be necessary to obtain a proper static response. It is concluded that even parity for the damping has to be preferred from the theoretical point of view, although odd and asymmetric parity yield virtually the same polarizability. The electromagnetic response can still be written in terms of a single complex frequency, in agreement with the requirements of electrodynamics. The resulting expression is suited for the treatment of nonisotropic systems.