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.