Long-wavelength quantum and classical plasma frequencies in fractional-dimensionalspace

Abstract

Long-wavelength plasma frequencies have been obtained in the modified random phaseapproximation (RPA) and plasmon-pole approximation (PPA) methods for both quantumand classical plasmas in fractional-dimensional space. The dynamical local-field factor isincluded in the dielectric function. Comparison of the plasma frequencies in these methodsshows that both RPA and PPA methods are quite accurate in finding plasma frequencies.Although the contribution of the dynamical local-field factor to the quantum plasmafrequency is quite significant, it vanishes for the classical plasma. While the quantumplasma is undamped in the collective excitation regime, the classical plasma is damped inthis regime.