• Corpus ID: 212675171

Wave Turbulence in Self-Gravitating Bose Gases

@article{Skipp2020WaveTI,
  title={Wave Turbulence in Self-Gravitating Bose Gases},
  author={Jonathan Skipp and Victor S. L’vov and Sergey Nazarenko},
  journal={arXiv: Statistical Mechanics},
  year={2020}
}

• J. Skipp, V. L’vov, S. Nazarenko
• Published 11 March 2020
• Physics, Mathematics
• arXiv: Statistical Mechanics

We develop the theory of weak wave turbulence in systems described by the Schrodinger-Helmholtz equation in two and three dimensions. This model contains as limits both the familiar cubic nonlinear Schrodinger equation, and the Schrodinger-Newton equations, the latter being a nonrelativistic model of Fuzzy Dark Matter which has a nonlocal gravitational self-potential. We show that in the weakly-nonlinear limit the Schrodinger-Helmholtz equation has a simultaneous inverse cascade of particles and a forward cascade of energy. The inverse cascade we interpret as a nonequilibrium condensation process, which could be a precursor to collapses and structure formation at large scales (for example the formation of galactic dark matter haloes). We show that for the Schrodinger-Newton equation in two and three dimensions, and in the two-dimensional nonlinear Schrodinger equation, the particle and energy fluxes are carried by small deviations from thermodynamic distributions, rather than the Kolmogorov-Zakharov cascades that are familiar in wave turbulence. We develop a differential approximation model to characterise such "warm cascade" states.