FREQUENCY-DEPENDENT SUSCEPTIBILITY OF A FREE-ELECTRON GAS IN D DIMENSIONS

The real and imaginary parts of the dynamic susceptibility of a free electron gas at T = 0 are obtained as a function of wave vector k, frequency ω, and space dimensionality D. The real part of the dynamic susceptibility is shown to be simply related to the static susceptibility. For odd-numbered dimensions there exists a general dimensional relationship for the dynamic susceptibility, originating from a similar relationship for the static susceptibility. For even-numbered dimensions there is no such general relationship, but instead a restricted one. © 1990 American Institute of Physics.