Long-wavelength quantum and classical plasma frequencies in fractional-dimensional space

Long-wavelength plasma frequencies have been obtained in the modified random phase approximation (RPA) and plasmon-pole approximation (PPA) methods for both quantum and classical plasmas in fractional-dimensional space. The dynamical local-field factor is included in the dielectric function. Comparison of the plasma frequencies in these methods shows 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 plasma frequency is quite significant, it vanishes for the classical plasma. While the quantum plasma is undamped in the collective excitation regime, the classical plasma is damped in this regime.

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