Weak and strong turbulence in self-focusing and defocusing media
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917898730078208 |
|---|---|
| author | Rosenhaus, Vladimir Falkovich, Gregory |
| author_facet | Rosenhaus, Vladimir Falkovich, Gregory |
| contents | While the focusing and defocusing Nonlinear Schrodinger Equations have similar behavior in the weak turbulence regime, they must differ dramatically in the strong turbulence regime. Here, we show that this difference is already present at next-to-leading order in the nonlinearity in the weak turbulence regime: The one-loop correction to the interaction vertex suppresses repulsion (like screening in electrodynamics), leading to a steeper spectrum in the defocusing case. In contrast, attraction enhancement (like antiscreening in chromodynamics) makes the spectrum less steep in the focusing case. To describe strong turbulence, we consider a vector model in the limit of a large number of components. A large-N kinetic equation, valid at all scales, can be derived analytically. It has an inverse-cascade solution whose two asymptotics, at high and low wavenumbers, describe weak and strong turbulence, respectively. We find two forms of universality in the strong turbulence spectrum: in focusing media it is independent of the flux magnitude, while in defocusing media it is independent of the bare coupling constant, with the largest scale appearing instead. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_12451 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Weak and strong turbulence in self-focusing and defocusing media Rosenhaus, Vladimir Falkovich, Gregory Fluid Dynamics Quantum Gases High Energy Physics - Theory Chaotic Dynamics While the focusing and defocusing Nonlinear Schrodinger Equations have similar behavior in the weak turbulence regime, they must differ dramatically in the strong turbulence regime. Here, we show that this difference is already present at next-to-leading order in the nonlinearity in the weak turbulence regime: The one-loop correction to the interaction vertex suppresses repulsion (like screening in electrodynamics), leading to a steeper spectrum in the defocusing case. In contrast, attraction enhancement (like antiscreening in chromodynamics) makes the spectrum less steep in the focusing case. To describe strong turbulence, we consider a vector model in the limit of a large number of components. A large-N kinetic equation, valid at all scales, can be derived analytically. It has an inverse-cascade solution whose two asymptotics, at high and low wavenumbers, describe weak and strong turbulence, respectively. We find two forms of universality in the strong turbulence spectrum: in focusing media it is independent of the flux magnitude, while in defocusing media it is independent of the bare coupling constant, with the largest scale appearing instead. |
| title | Weak and strong turbulence in self-focusing and defocusing media |
| topic | Fluid Dynamics Quantum Gases High Energy Physics - Theory Chaotic Dynamics |
| url | https://arxiv.org/abs/2501.12451 |