Abstract
We develop the theory of weak wave turbulence in systems described by the Schrödinger-Helmholtz equations in two and three dimensions. This model contains as limits both the familiar cubic nonlinear Schrödinger equation, and the Schrödinger-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 Schrödinger-Helmholtz equations have a simultaneous inverse cascade of particles and a forward cascade of energy. The inverse cascade we interpret 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 Schrödinger-Newton equations in two and three dimensions, and in the two-dimensional nonlinear Schrödinger 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 characterize such "warm cascade"states.
Original language | English |
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Article number | 043318 |
Number of pages | 20 |
Journal | Physical Review A |
Volume | 102 |
Issue number | 4 |
DOIs | |
Publication status | Published - Oct 2020 |
Bibliographical note
S.N. and J.S. thank Marc Brachet for useful discussions regarding the Jeans swindle and its resolution. S.N. is supported by the Chaire D'Excellence IDEX (Initiative of Excellence) awarded by Université de la Côte d'Azur, France, the EU Horizon 2020 research and innovation programme under the Grant Agreements No. 823937 in the framework of Marie Skodowska-Curie HALT project and Grant No. 820392 in the FET Flagships PhoQuS project, and the Simons Foundation Collaboration grant “Wave Turbulence” (Award ID 651471). J.S. is supported by the UK EPSRC through Grant No. EP/I01358X/1.All Science Journal Classification (ASJC) codes
- Atomic and Molecular Physics, and Optics