Harmonic generation by one-dimensional systems

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Abstract
The authors consider harmonic generation by one-dimensional systems and low frequency periodic electric fields; they provide a detailed description of the classical dynamics of an arbitrary system, but treat the quantal dynamics in less detail indicating only those regions where the two dynamics either produce similar results or are quite different. They express the Hamiltonian in an adiabatic representation, which has the correct limit as the field frequency tends to zero; this enables them to show that for very low frequency fields the classical and quantal mechanisms of harmonic generation are the same. The non-adiabatic correction terms may manifest themselves in different manners according to whether a classical or a quantal description is used. In the classical case, they provide an analytic description of the motion of an arbitrary system valid for fields which do not ionize the system and have sufficiently low frequency; they apply this theory to a one-dimensional hydrogen atom. In the quantal case we provide a more approximate description. The results, which are system independent, explain many features of extant numerical calculations.