FORMULATION OF NONLINEAR CONDUCTIVITY IN A MANY-ELECTRON SYSTEM IN THE PRESENCE OF AN OSCILLATORY ELECTRIC-FIELD BY A COMBINED PROJECTION TECHNIQUE

A non-linear form for the current in a many-electron system which is subject to an oscillatory electric field is derived by starting with the Liouville equation and with the help of the combined projection technique which combines the techniques of Kenkre and of Argyres and Sigel. The primary projection operator yields the general expression for the current in the Fourier-Laplace transformed space. The secondary combined projection operator generates the lowest order of non-linearity in the expression. The final result is given in a time-retarded form, but not in a continued-fraction form.