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Abstract
We propose a new application of random tensor theory to studies of nonlinear random flows in many variables. Our focus is on nonlinear resonant systems which often emerge as weakly nonlinear approximations to problems whose linearized perturbations possess highly resonant spectra of frequencies (nonlinear Schrödinger equations for Bose–Einstein condensates in harmonic traps, dynamics in Antide Sitter spacetimes, etc). We perform Gaussian averaging both for the tensor coupling between modes and for the initial conditions. In the limit when the initial configuration has many modes excited, we prove that there is a leading regime of perturbation theory governed by the melonic graphs of random tensor theory. Restricting the flow equation to the corresponding melonic approximation, we show that at least during a finite time interval, the initial excitation spreads over more modes, as expected in a turbulent cascade. We call this phenomenon melonic turbulence.
Original language  English 

Article number  374 
Pages (fromto)  11791228 
Number of pages  54 
Journal  Comm. Math. Phys. 
Volume  374 
Issue number  2 
DOIs  
Publication status  Published  Mar 2020 
Bibliographical note
54 pages, 20 figuresKeywords
 mathph
 hepth
 math.AP
 math.MP
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 1 Active

SRP8: Strategic Research Programme: HighEnergy Physics at the VUB
D'Hondt, J., Van Eijndhoven, N., Craps, B. & Buitink, S.
1/11/12 → 31/10/22
Project: Fundamental