Fetching the paper…

Reading the bibliography…

2017

Maximally rotating waves in AdS and on spheres

Craps, Ben, Evnin, Oleg, Luyten, Vincent

Original
PDF
Post on X

Understand

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).

Maximally rotating waves in AdS and on spheres · Around

Built on

U. Niederer, The maximal kinematical invariance group of the harmonic oscillator, Helv. Phys. Acta 46
1973
Earlier work this paper cites.
J. A. Murdock, Perturbations: Theory and Methods
1987
Earlier work this paper cites.
A. Karch and E. Katz, Adding flavor to AdS/CFT, JHEP 0206
2002
Earlier work this paper cites.
T. Sakai and S. Sugimoto, Low energy hadron physics in holographic QCD, Prog. Theor. Phys. 113
2005
Earlier work this paper cites.
I. Bloch, J. Dalibard and W. Zwerger, Many-body physics with ultracold gases , Rev. Mod. Phys. 80
Original
2008
Earlier work this paper cites.
N. R. Cooper, Rapidly rotating atomic gases , Adv. Phys. 57 (2008) 539 arXiv:0810.4398 [cond-mat.mes-hall]
Original
2008
Earlier work this paper cites.
S. A. Hartnoll, C. P. Herzog and G. T. Horowitz, Building a Holographic Superconductor, Phys. Rev. Lett. 101
Original
2008
Earlier work this paper cites.
A. L. Fetter, Rotating trapped Bose-Einstein condensates , Rev. Mod. Phys. 81
Original
2009
Earlier work this paper cites.
P. Gérard and S. Grellier, The cubic Szegő equation,
Original
2010
Earlier work this paper cites.

Similar

T. Nishioka, S. Ryu and T. Takayanagi, Holographic Superconductor/Insulator Transition at Zero Temperature, JHEP 1003
Original
2010
Cited alongside, same era.
P. Bizoń and A. Rostworowski, On weakly turbulent instability of anti-de Sitter space,
Original
2011
Cited alongside, same era.
P. Basu and S. R. Das, Quantum Quench across a Holographic Critical Point, JHEP 1201
Original
2012
Cited alongside, same era.
P. Basu, D. Das, S. R. Das and T. Nishioka, Quantum Quench Across a Zero Temperature Holographic Superfluid Transition, JHEP 1303
Original
2013
Cited alongside, same era.
V. Balasubramanian, A. Buchel, S. R. Green, L. Lehner and S. L. Liebling, Holographic Thermalization, Stability of Anti-de Sitter Space, and the Fermi-Pasta-Ulam Paradox, Phys. Rev. Lett. 113

Then

O. Evnin and C. Krishnan, A Hidden Symmetry of AdS Resonances, Phys. Rev. D 91
Original
2015
Later among the works it cites.
B. Craps and O. Evnin, AdS (in)stability: an analytic approach,
Original
2016
Later among the works it cites.
P. Germain, Z. Hani, and L. Thomann, On the continuous resonant equation for NLS: I. Deterministic analysis, J. Math. Pur. App. 105
Original
2016
Later among the works it cites.
P. Germain and L. Thomann, On the high frequency limit of the LLL equation , Quart. Appl. Math. 74
Original
2016
Later among the works it cites.
O. Evnin and R. Nivesvivat, AdS perturbations, isometries, selection rules and the Higgs oscillator, JHEP 1601

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

Original

2014

Cited alongside, same era.

B. Craps, O. Evnin and J. Vanhoof, Renormalization group, secular term resummation and AdS (in)stability, JHEP 1410

2014

Cited alongside, same era.

B. Craps, O. Evnin and J. Vanhoof, Renormalization, averaging, conservation laws and AdS (in)stability, JHEP 1501

2015

Cited alongside, same era.

P. Basu, C. Krishnan and A. Saurabh, A Stochasticity Threshold in Holography and the Instability of AdS, Int. J. Mod. Phys. A 30

Original

2015

Cited alongside, same era.

I-S. Yang, Missing top of the AdS resonance structure, Phys. Rev. D 91

2015

Cited alongside, same era.

A. Biasi, P. Bizoń, B. Craps and O. Evnin, Exact LLL Solutions for BEC Vortex Precession, arXiv:1705.00867 [cond-mat.quant-gas]

Cited in the paper.

O. J. C. Dias and J. E. Santos, AdS nonlinear instability: breaking spherical and axial symmetries, arXiv:1705.03065 [hep-th]

Cited in the paper.

M. W. Choptuik, O. J. C. Dias, J. E. Santos and B. Way, Collapse and Nonlinear Instability of AdS with Angular Momenta, arXiv:1706.06101 [hep-th]

Cited in the paper.

2016

Later among the works it cites.

P. Bizoń, B. Craps, O. Evnin, D. Hunik, V. Luyten and M. Maliborski, Conformal flow on S 3 S^{3} and weak field integrability in AdS 4 , Comm. Math. Phys. 353

2017

Closest in time.

A. Rostworowski, Higher order perturbations of anti-de Sitter space and time-periodic solutions of vacuum Einstein equations, Phys. Rev. D 95

2017

Closest in time.

G. Martinon, G. Fodor, P. Grandclément and P. Forgàcs, Gravitational geons in asymptotically anti-de Sitter spacetimes, Class. Quant. Grav. 34

2017

Closest in time.

A. F. Biasi, J. Mas and A. Paredes, Delayed collapses of Bose-Einstein condensates in relation to anti-de Sitter gravity, Phys. Rev. E 95

2017

Closest in time.