Resonant Hamiltonian systems and weakly nonlinear dynamics in AdS spacetimes

Weakly nonlinear dynamics in anti-de Sitter (AdS) spacetimes is reviewed, keeping an eye on the AdS instability conjecture and focusing on the resonant approximation that accurately captures in a simplified form the long-term evolution of small initial data. Topics covered include turbulent and regu...

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Bibliographic Details
Published in:Classical and quantum gravity 2021-10, Vol.38 (20), p.203001
Main Author: Evnin, Oleg
Format: Article
Language:English
Subjects:
gravitational dynamics
integrable motion
multiscale analysis
quantum chaos theory
resonant bounded domains
symmetry-based selection rules
weak turbulence
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Summary:Weakly nonlinear dynamics in anti-de Sitter (AdS) spacetimes is reviewed, keeping an eye on the AdS instability conjecture and focusing on the resonant approximation that accurately captures in a simplified form the long-term evolution of small initial data. Topics covered include turbulent and regular motion, dynamical recurrences analogous to the Fermi–Pasta–Ulam phenomena in oscillator chains, and relations between AdS dynamics and nonrelativistic nonlinear Schrödinger equations in harmonic potentials. Special mention is given to the way the classical dynamics of weakly nonlinear strongly resonant systems is illuminated by perturbative considerations within the corresponding quantum theories, in particular, in relation to quantum chaos theory.
ISSN:0264-9381
1361-6382
DOI:10.1088/1361-6382/ac1b46