Maximally rotating waves in AdS and on spheres
arXiv:1707.08501 · doi:10.1007/JHEP09(2017)059
Abstract
We study the cubic wave equation in AdS_(d+1) (and a closely related cubic wave equation on S^3) in a weakly nonlinear regime. Via time-averaging, these systems are accurately described by simplified infinite-dimensional quartic Hamiltonian systems, whose structure is mandated by the fully resonant spectrum of linearized perturbations. The maximally rotating sector, comprising only the modes of maximal angular momentum at each frequency level, consistently decouples in the weakly nonlinear regime. The Hamiltonian systems obtained by this decoupling display remarkable periodic return behaviors closely analogous to what has been demonstrated in recent literature for a few other related equations (the cubic Szego equation, the conformal flow, the LLL equation). This suggests a powerful underlying analytic structure, such as integrability. We comment on the connection of our considerations to the Gross-Pitaevskii equation for harmonically trapped Bose-Einstein condensates.
arXiv comment17 pages
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Cited by in corpus (17)
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- Two infinite families of resonant solutions for the Gross-Pitaevskii equation
- Resonant Hamiltonian systems and weakly nonlinear dynamics in AdS spacetimes
- Solvable cubic resonant systems
- A nonrelativistic limit for AdS perturbations
- Quantum resonant systems, integrable and chaotic
- Fermi-Pasta-Ulam phenomena and persistent breathers in the harmonic trap
- Energy level splitting for weakly interacting bosons in a harmonic trap
- Complex plane representations and stationary states in cubic and quintic resonant systems
- Energy returns in global AdS_4
- Turbulent cascades in a truncation of the cubic Szego equation and related systems
- Melonic Turbulence
- Time-periodicities in holographic CFTs
- Exact solutions for a coherent phenomenon of condensation in conservative Hamiltonian systems
- Energy cascades and condensation via coherent dynamics in Hamiltonian systems
- A superintegrable quantum field theory