The quantum cubic Szegő equation exhibits integer spectra for its Hamiltonian and conserved hierarchies, indicating superintegrability beyond ordinary quantum integrability.
Resonant dynamics and the instability of anti-de Sitter spacetime
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abstract
We consider spherically symmetric Einstein-massless-scalar field equations with negative cosmological constant in five dimensions and analyze evolution of small perturbations of anti-de Sitter spacetime using the recently proposed resonant approximation. We show that for typical initial data the solution of the resonant system develops an oscillatory singularity in finite time. This result hints at a possible route to establishing instability of AdS under arbitrarily small perturbations.
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A superintegrable quantum field theory
The quantum cubic Szegő equation exhibits integer spectra for its Hamiltonian and conserved hierarchies, indicating superintegrability beyond ordinary quantum integrability.