Abstract
In this paper, we calculate a self-contained theoretical analysis of the dynamical response of the electron system in the fractional dimensional space within the random phase approximation. We find the static response function in several integer and non-integer dimensions. The plasma frequencies except in the quasi-one-dimensional system are damped into particle–hole excitation. In the long-wavelength limit the plasma frequency is finite at zero wave vector in three-dimensional system while these vanish at the same wave vector in the lower-dimensional systems.
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