Schrödinger-Poisson solitons: Perturbation theory

Self-gravitating quantum matter may exist in a wide range of cosmological and astrophysical settings from the very early universe through to present-day boson stars. Such arises number different theories, including Peccei-Quinn axion UltraLight (ULDM) or Fuzzy (FDM) dark scenarios. We consider dynamical evolution perturbations spherically symmetric soliton, ground state solution Schr\"{o}dinger-Poisson system common all these construct eigenstates Schr\"{o}dinger equation, holding gravitational potential fixed its value. see that qualitatively capture properties seen full ULDM simulations, soliton "breathing" mode, random walk center, quadrupolar distortions soliton. then show time-evolution impact on can be well described within framework time-dependent perturbation theory. Applying our formalism synthetic halo reveals considerable mixing eigenstates, even though overall density profile is relatively stable. Our results provide new analytic approach understanding systems as possibilities for faster approximate simulations.