Statistical description of interacting multistream quantum systems

Abstract

In this research, the electrostatically coupled multistream quasiparticle excitations are studied in the framework of the Wigner distribution function. It is remarked that the Wigner distribution of coupled multistream collective quantum excitations satisfies a simple Liouville-like evolution equation from which a generalized distribution function for multistream quasiparticle excitations is deduced. The phase-space structure of collective quantum excitations in counter-stream electron and two-stream electron–positron gas with their evolution is calculated and electron/positron hole formation due to the onset of quantum stream instability is studied in connection with the energy band structure of the multistream quantum system, for the first time. The quantum stream instabilities in symmetric and asymmetric stream systems are studied and compared. It is found that the presence of opposite-charge streams leads to overall stability due to lowering the interaction potential effect. The generalized Wigner theory is also applied to study the electron transport in a one-dimensional periodic lattice using the concept of virtual streams. Current generalized statistical formalism may be used to model different quantum phenomena in the linear excitations limit with collective electrostatic interactions. The applications extend to the stream instability in quantum charge transport in metals, semiconductors, plasmonic devices, phase-space structure of charge carriers in periodic lattices interacting with the external potential of arbitrary shape and the dynamic evolution of dense electron–positron jets in active galactic nuclei or within the extremely dense astrophysical objects.