2021/04/30 by Oleg Evnin
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Conjecture #Dynamics (music) #Hamiltonian (control theory) #Harmonic oscillator #Instability #Nonlinear system #Quantum #Quantum Electrodynamics and Casimir Effect #Quantum Mechanics and Non-Hermitian Physics #gr-qc #hep-th #math-ph #math.AP #math.MP
paper · pdf · doi:10.1088/1361-6382/ac1b46
published as Class. Quant. Grav. 38 (2021) 203001 · topical review for Clas. Quant. Grav; v2: slightly expanded, accepted for publication
openalex created_date 2021/04/26 · openalex publication_date 2021/08/06 · arxiv created 2021/08/07 · arxiv updated 2021/09/24 · openalex updated_date 2026/08/05
Abstract 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.