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Abstract
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In this research, we calculate the heat capacity and electrical conductivity of plasmon excitations in an arbitrary degenerate electron gas by
using the linearized Schr€ odinger-Poisson model. It is shown that the large heat capacity of electron fluid such as in metals can be attributed
to the collective excitations. These excitations unlike those for low energy fermion excitations dominant at low temperatures follow the BoseEinstein statistics and contribute significantly at higher temperatures where a significant number of electrons excite to energy levels beyond
twice the plasmon energy of electron fluid. The current density and electrical conductivity of plasmon excitations in the current model show
unique features for characteristic current-voltage and their temperature dependence. It is found that a single electron fermion excitation
model such as the one used in free electron assumption is not appropriate for a full description of electron contribution to the physical properties of metals and plasmas at very high temperatures. The coupled pseudoforce system with a periodic density structure in the presence of
a uniform electric field is also considered with appropriate boundary conditions to evaluate the characteristic aspects of collective excitations
in a one dimensional plasmonic crystal. The application of the lattice periodicity on the wavefunction and the electrostatic potential results
in singularities for the probability current due to plasmon excitations. It is shown that such an effect persists with an arbitrary ion core potential function which obeys the lattice periodicity. The current model clearly demonstrates the importance of collective electronic excitation in
the physical properties of electron gas with an arbitrary degree of degeneracy
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