Collective gravitational quantum excitations in fuzzy dark matter

In this paper, we investigate collective quantum excitations in fuzzy dark matter (FDM) within the framework of the dual-length-scale quasiparticle excitation model. The Schrödinger–Poisson system is employed to examine the matter wave dispersion of both relativistic and nonrelativistic gravitational quantum (GQ) excitations in FDM, which consists of light-mass bosons with an approximate Compton wavelength of one light year. Using the generalized matter wave dispersion, we explore various thermodynamic properties of FDM. Analyzing the energy density of nonrelativistic GQ excitations reveals fundamental differences in energy and particle distributions across distinct regimes of collapse, stability, and expansion orbitals. These GQ regimes arise due to the delicate interplay between the wave-like and particle-like nature of excitations. We derive an expression for the temporal evolution of dynamic-density, incorporating interaction potential effects, from which the Landau-like collisionless quantum lifetime of excited GQ states into equilibrium can be determined. Furthermore, the evaluation of statistically averaged potential energy and density around a gravitational pole exhibits similarities between polar number density distribution dependencies on the FDM chemical potential and temperature, akin to the well-known Friedel oscillations in electron gas. Our study highlights intriguing gravitational pole screening phenomena, including the formation of gravitational potential oscillations, as well as attractive and repulsive gravitational potential regions that can drive structure formation on cosmological scales and contribute to galactic evolution. Additionally, FDM density variations may imprint structural details onto the gravitational lensing phenomenon, offering new insights into large-scale cosmic dynamics. Finally, we propose a new approach for analyzing quantum aspects of binary dynamics and black hole mergers based on the time-dependent evolution of the modified Wigner distribution.