Incoherent localized structures and hidden coherent solitons from the gravitational instability of the Schrödinger-Poisson equation
arXiv:2108.13250
Abstract
The long-term behavior of a modulationally unstable conservative nonintegrable system is known to be characterized by the soliton turbulence self-organization process. We consider this problem in the presence of a long-range interaction in the framework of the Schrödinger-Poisson (or Newton-Schrödinger) equation accounting for the gravitational interaction. By increasing the amount of nonlinearity, the system self-organizes into a large-scale incoherent localized structure that contains "hidden" coherent soliton states: The solitons can hardly be identified in the usual spatial or spectral domains, while their existence is unveiled in the phase-space representation (spectrogram). We develop a theoretical approach that provides the coupled description of the coherent soliton component (governed by an effective Schrödinger-Poisson equation) and of the incoherent component (governed by a wave turbulence Vlasov-Poisson equation). The theory shows that the incoherent structure introduces an effective trapping potential that stabilizes the hidden coherent soliton, a mechanism that we verify by direct numerical simulations. The theory characterizes the properties of the localized incoherent structure, such as its compactly supported spectral shape. It also clarifies the quantum-to-classical correspondence in the presence of gravitational interactions. This study is of potential interest for self-gravitating Boson models of fuzzy dark matter. Although we focus our paper on the Schrödinger-Poisson equation, we show that our results are general for long-range wave systems characterized by an algebraic decay of the interacting potential. This work should stimulate nonlinear optics experiments in highly nonlocal nonlinear (thermal) media that mimic the long-range nature of gravitational interactions.
arXiv comment23 pages, 6 figures
References in corpus (45)
- The Cosmological Constant and Dark Energy
- Simulating the joint evolution of quasars, galaxies and their large-scale distribution
- Cold and Fuzzy Dark Matter
- Ultralight scalars as cosmological dark matter
- Small-Scale Challenges to the CDM Paradigm
- Statistical mechanics and dynamics of solvable models with long-range interactions
- Cosmic Structure as the Quantum Interference of a Coherent Dark Wave
- Observation of optical spatial solitons in a highly nonlocal medium
- Understanding the Core-Halo Relation of Quantum Wave Dark Matter, DM, from 3D Simulations
- Mass-radius relation of Newtonian self-gravitating Bose-Einstein condensates with short-range interactions: I. Analytical results
- Cold dark matter: controversies on small scales
- Modulational instability, solitons and beam propagation in spatially nonlocal nonlinear media
- Galaxy Formation with BECDM: I. Turbulence and relaxation of idealised haloes
- Hybrid photonic-crystal fiber
- Simulations of solitonic core mergers in ultra-light axion dark matter cosmologies
- Mass-radius relation of Newtonian self-gravitating Bose-Einstein condensates with short-range interactions: II. Numerical results
- Gravitational Bose-Einstein condensation in the kinetic regime
- Galactic Halos As Boson Stars
- Formation and structure of ultralight bosonic dark matter halos
- Shocks in nonlocal media
- The laminar-turbulent transition in a fibre laser
- Gravitational cooling of self-gravitating Bose-Condensates
- Galactic Rotation Curves vs. Ultra-Light Dark Matter: Implications of the Soliton -- Host Halo Relation
- Nonlocal stabilization of nonlinear beams in a self-focusing atomic vapor
- First star-forming structures in fuzzy cosmic filaments
- The Schrödinger-Newton equation as non-relativistic limit of self-gravitating Klein-Gordon and Dirac fields
- Formation and mass growth of axion stars in axion miniclusters
- On the Schrodinger-Poisson--Vlasov-Poisson correspondence
- Rayleigh-Jeans condensation of classical light : Observation and thermodynamic characterization
- Vortices and turbulence in trapped atomic condensates
- Dramatic acceleration of wave condensation mediated by disorder in multimode fibers
- Formation, Gravitational Clustering and Interactions of Non-relativistic Solitons in an Expanding Universe
- Optical wave turbulence and condensation of light
- Schrödinger method as N-body double and UV completion of dust
- Soliton Random Walk and the Cluster-Stripping Problem in Ultralight Dark Matter
- Self-organization in nonlinear wave turbulence
- Energy cascade with small-scales thermalization, counterflow metastability and anomalous velocity of vortex rings in Fourier-truncated Gross-Pitaevskii equation
- The role of geometry in the superfluid flow of nonlocal photon fluids
- Derivation of the core mass -- halo mass relation of fermionic and bosonic dark matter halos from an effective thermodynamical model
- Localization and Coherence in Nonintegrable Systems
- Spatial solitons in thermo-optical media from the nonlinear Schrodinger-Poisson equation and dark matter analogues
- Acoustic black-hole bombs and scalar clouds in a photon-fluid model
- Massive phonons and gravitational dynamics in a photon-fluid model
- Wave turbulence in self-gravitating Bose gases and nonlocal nonlinear optics
- Coherent soliton states hidden in phase-space and stabilized by gravitational incoherent structures