Kinetic Theory of Fermi-Boson Systems

The collective dynamics of strongly interacting quantum matter, where fermionic carriers and bosonic excitations coexist and mutually influence one another, represent a challenging and rapidly growing active field in theoretical physics. While the hydrodynamic and Vlasov limits are well established for Fermi-Dirac systems, a fully self-consistent treatment that places species of differing natures on equal footing remains largely unexplored. This work addresses that gap by going beyond the mean-field truncation of the BBGKY hierarchy, explicitly quantizing the collective charge oscillations and promoting the resulting plasmons to a dynamical bosonic species governed by their own kinetic equation, coupled to the fermionic sector through effective inter-species force terms.

The framework is applied to two-dimensional Dirac materials, specifically monolayer graphene, whose linear band structure and gapless plasmonic spectrum make it a natural platform for this study. The thermodynamic quantities of both sectors are derived to construct the fermion-boson coupling via ponderomotive and refractive forces, and from the resulting multispecies secular determinant, the collective mode spectrum is extracted via energy-loss function.

A modified plasmon mode is found, shifted in frequency and intrinsically damped through the complex bosonic polarizability, with a charge-oscillation character confirmed by mode decomposition. A second spectral feature is analytically identified as an anti-resonance and a closed-form dispersion relation is derived for it. Finally, kinetic simulations uncover a sound-like instability with non-zero real frequency and positive growth rate, absent in the bare fermionic system. Theory and simulation agree across a range of parameters, for which it was determined that the sound mode develops curvature at large μ/kBT >> 1.