Time and frequency dependent behavior of a two dimensional electron gas at long wavelengths

Using the recently developed method of recurrence relations, we have studied the time and frequency dependent behavior of the two dimensional electronic system at long wavelengths. Several families of autocorrelation functions including the relaxation and memory functions are obtained exactly. In addition, other linear response quantities e.g., the density-density response function and dynamic structure factor are obtained. This work contains a detailed application of the method of recurrence relations.