Universal regimes of strong turbulence in the multi-component Gross-Pitaevskii model
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| Format: | Preprint |
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2025
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| _version_ | 1866909910495657984 |
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| author | Rosenhaus, Vladimir Vladimirova, Natalia Falkovich, Gregory |
| author_facet | Rosenhaus, Vladimir Vladimirova, Natalia Falkovich, Gregory |
| contents | The Gross-Pitaevskii (GP) model, also known as the nonlinear Schrödinger equation, is arguably the most universal model in classical and quantum physics, describing spectrally narrow or long-wavelength distributions of interacting waves or particles. Modern applications -- from oceanic and atmospheric flows to photonics and cold atoms -- predominantly involve states that are far from equilibrium, culminating in the regime of fully developed turbulence. To date, a consistent theoretical description of such states has only existed for weakly interacting quasiparticles. Here we present a theory of strong turbulence in the two-dimensional $N$-component Gross-Pitaevskii model for both repulsive and attractive interactions, corresponding to the defocusing and focusing cases, respectively. In the focusing case, we show that attraction is enhanced by multi-wave effects, leading to a critical-balance state independent of the pumping level. In the defocusing case, repulsion is suppressed by collective effects, giving rise to another type of universality in strong turbulence -- independence from the bare coupling constant. The theory is confirmed by analytical results in the many-component limit and by direct numerical simulations of the single-component GP model. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_14068 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Universal regimes of strong turbulence in the multi-component Gross-Pitaevskii model Rosenhaus, Vladimir Vladimirova, Natalia Falkovich, Gregory Quantum Gases High Energy Physics - Theory Chaotic Dynamics Fluid Dynamics Plasma Physics The Gross-Pitaevskii (GP) model, also known as the nonlinear Schrödinger equation, is arguably the most universal model in classical and quantum physics, describing spectrally narrow or long-wavelength distributions of interacting waves or particles. Modern applications -- from oceanic and atmospheric flows to photonics and cold atoms -- predominantly involve states that are far from equilibrium, culminating in the regime of fully developed turbulence. To date, a consistent theoretical description of such states has only existed for weakly interacting quasiparticles. Here we present a theory of strong turbulence in the two-dimensional $N$-component Gross-Pitaevskii model for both repulsive and attractive interactions, corresponding to the defocusing and focusing cases, respectively. In the focusing case, we show that attraction is enhanced by multi-wave effects, leading to a critical-balance state independent of the pumping level. In the defocusing case, repulsion is suppressed by collective effects, giving rise to another type of universality in strong turbulence -- independence from the bare coupling constant. The theory is confirmed by analytical results in the many-component limit and by direct numerical simulations of the single-component GP model. |
| title | Universal regimes of strong turbulence in the multi-component Gross-Pitaevskii model |
| topic | Quantum Gases High Energy Physics - Theory Chaotic Dynamics Fluid Dynamics Plasma Physics |
| url | https://arxiv.org/abs/2511.14068 |