A simple DFT proposed model for charged particles in arbitrary spatial dimensions: Thermodynamic excitations

An analytical functional is established for the interaction of charged particles in arbitrary spatial dimensions, whether fractional or not, specifically for the ground state. Upon extremizing this functional, the resulting background energy becomes dependent on both dimension and the density of charged particles. Notably, in low spatial dimensions, the kinetic and Coulomb contributions exhibit distinct differences. Taking into account external disturbances and temperature effects, we evaluate the lifetime of elementary excitations. This lifetime is directly linked to the mobility and diffusion coefficient, showing an increase with spatial dimension. Furthermore, we determine the entropy of the excitations under the assumption of scale invariance (fractons). Interesting, depending on energy, the entropy either grows or decreases with spatial dimension, establishing a robust connection between dimension and temperature. Connecting the spatial dimension to the Coulomb contribution, we find that the residual entropy associated with the spatial dimension reveals an inflection point indicative of a phase transition around dimension two.