Asymptotic behaviour and general properties of harmonic generation susceptibilities

We use the Kubo response function formalism to derive the asymptotic behaviour of the harmonic generation susceptibilities to all orders n. The results show a, stringent correspondence with the ones previously obtained from the classical anharmonic oscillator model. They are characterized by a omega (-2n-2) dependence and a coefficient proportional to the trace of the (n + 1)th derivative of the potential energy on the equilibrium density matrix. Using the above results we derive new Kramers-Kronig relations and sum rules for all orders of harmonics susceptibilities.