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arXiv · 2003.05558

Wave turbulence in self-gravitating Bose gases and nonlocal nonlinear optics

Jonathan Skipp·Victor L'vov·Sergey Nazarenko
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Abstract

We develop the theory of weak wave turbulence in systems described by the Schr\"odinger-Helmholtz equations in two and three dimensions. This model contains as limits both the familiar cubic nonlinear Schr\"odinger equation, and the Schr\"odinger-Newton equations. The latter, in three dimensions, are a nonrelativistic model of fuzzy dark matter which has a nonlocal gravitational self-potential, and in two dimensions they describe nonlocal nonlinear optics in the paraxial approximation. We show that in the weakly nonlinear limit the Schr\"odinger-Helmholtz equations have a simultaneous inverse cascade of particles and a forward cascade of energy. We interpret the inverse cascade as a nonequilibrium condensation process, which is a precursor to structure formation at large scales (for example the formation of galactic dark matter haloes or optical solitons). We show that for the Schr\"odinger-Newton equations in two and three dimensions, and in the two-dimensional nonlinear Schr\"odinger 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.

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BibTeXRIS

Jonathan Skipp, Victor L'vov, Sergey Nazarenko. 2020-03-11. Wave turbulence in self-gravitating Bose gases and nonlocal nonlinear optics. https://doi.org/10.1103/physreva.102.043318

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