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| Main Authors: | , |
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| Format: | Preprint |
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2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2406.18475 |
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| _version_ | 1866929400707022848 |
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| author | Rosenhaus, Vladimir Schubring, Daniel |
| author_facet | Rosenhaus, Vladimir Schubring, Daniel |
| contents | We study wave turbulence in systems with two special properties: a large number of fields (large $N$) and a nonlinear interaction that is strongly local in momentum space. The first property allows us to find the kinetic equation at all interaction strengths -- both weak and strong, at leading order in $1/N$. The second allows us to turn the kinetic equation -- an integral equation -- into a differential equation. We find stationary solutions for the occupation number as a function of wave number, valid at all scales. As expected, on the weak coupling end the solutions asymptote to Kolmogorov-Zakharov scaling. On the strong coupling end, they asymptote to either the widely conjectured generalized Phillips spectrum (also known as critical balance), or a Kolmogorov-like scaling exponent. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_18475 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Strong wave turbulence in strongly local large $N$ theories Rosenhaus, Vladimir Schubring, Daniel High Energy Physics - Theory High Energy Astrophysical Phenomena Statistical Mechanics Fluid Dynamics We study wave turbulence in systems with two special properties: a large number of fields (large $N$) and a nonlinear interaction that is strongly local in momentum space. The first property allows us to find the kinetic equation at all interaction strengths -- both weak and strong, at leading order in $1/N$. The second allows us to turn the kinetic equation -- an integral equation -- into a differential equation. We find stationary solutions for the occupation number as a function of wave number, valid at all scales. As expected, on the weak coupling end the solutions asymptote to Kolmogorov-Zakharov scaling. On the strong coupling end, they asymptote to either the widely conjectured generalized Phillips spectrum (also known as critical balance), or a Kolmogorov-like scaling exponent. |
| title | Strong wave turbulence in strongly local large $N$ theories |
| topic | High Energy Physics - Theory High Energy Astrophysical Phenomena Statistical Mechanics Fluid Dynamics |
| url | https://arxiv.org/abs/2406.18475 |