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Maximally rotating waves in AdS and on spheres. / Craps, Ben; Evnin, Oleg; Luyten, Vincent.

In: Journal of High Energy Physics, Vol. 2017, No. 9, 59, 14.09.2017.

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Craps, Ben ; Evnin, Oleg ; Luyten, Vincent. / Maximally rotating waves in AdS and on spheres. In: Journal of High Energy Physics. 2017 ; Vol. 2017, No. 9.

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@article{4e1a6815fa894d53ac315dd08b6cd069,
title = "Maximally rotating waves in AdS and on spheres",
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.",
keywords = "AdS-CFT Correspondence, Classical Theories of Gravity, Holography and condensed matter physics (AdS/CMT), Integrable Hierarchies",
author = "Ben Craps and Oleg Evnin and Vincent Luyten",
year = "2017",
month = "9",
day = "14",
doi = "10.1007/JHEP09(2017)059",
language = "English",
volume = "2017",
journal = "Journal of High Energy Physics",
issn = "1126-6708",
publisher = "Springer Verlag",
number = "9",

}

RIS

TY - JOUR

T1 - Maximally rotating waves in AdS and on spheres

AU - Craps, Ben

AU - Evnin, Oleg

AU - Luyten, Vincent

PY - 2017/9/14

Y1 - 2017/9/14

N2 - 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.

AB - 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.

KW - AdS-CFT Correspondence

KW - Classical Theories of Gravity

KW - Holography and condensed matter physics (AdS/CMT)

KW - Integrable Hierarchies

UR - http://www.scopus.com/inward/record.url?scp=85029692133&partnerID=8YFLogxK

U2 - 10.1007/JHEP09(2017)059

DO - 10.1007/JHEP09(2017)059

M3 - Article

VL - 2017

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

SN - 1126-6708

IS - 9

M1 - 59

ER -

ID: 34646814