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Abstract
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In this paper, using the quantum multistream model, we develop a method to study the electronic
band structure of plasmonic excitations in streaming electron gas with arbitrary degree of degeneracy.
The multifluid quantum hydrodynamic model is used to obtain N‑coupled pseudoforce differential
equation system from which the energy band structure of plasmonic excitations is calculated. It is
shown that inevitable appearance of energy bands separated by gaps can be due to discrete velocity
filaments and their electrostatic mode coupling in the electron gas. Current model also provides
an alternative description of collisionless damping and phase mixing, i.e., collective scattering
phenomenon within the energy band gaps due to mode coupling between wave‑like and particle‑like
oscillations. The quantum multistream model is further generalized to include virtual streams which is
used to calculate the electronic band structure of one‑dimensional plasmonic crystals. It is remarked
that, unlike the empty lattice approximation in free electron model, energy band gaps exist in
plasmon excitations due to the collective electrostatic interactions between electrons. It is also shown
that the plasmonic band gap size at first Brillouin zone boundary maximizes at the reciprocal lattice
vector, G, close to metallic densities. Furthermore, the electron‑lattice binding and electron‑phonon
coupling strength effects on the electronic band structure are discussed. It is remarked that inevitable
formation of energy band structure is a general characteristics of various electromagnetically and
gravitationally coupled quantum multistream systems.
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