KAM-Stability for Conserved Quantities in Finite-Dimensional Quantum Systems
arXiv:2011.04707 · doi:10.1103/PhysRevLett.126.150401
Abstract
We show that for any finite-dimensional quantum systems the conserved quantities can be characterized by their robustness to small perturbations: for fragile symmetries small perturbations can lead to large deviations over long times, while for robust symmetries their expectation values remain close to their initial values for all times. This is in analogy with the celebrated Kolmogorov-Arnold-Moser (KAM) theorem in classical mechanics. To prove this remarkable result, we introduce a resummation of a perturbation series, which generalizes the Hamiltonian of the quantum Zeno dynamics.
13 pages, 3 figures. Corrected typo in author name and added arXiv link to reference [16]
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Cited by in corpus (5)
- Weak and ultrastrong coupling limits of the quantum mean force Gibbs state
- One bound to rule them all: from Adiabatic to Zeno
- Probing Dynamical Sensitivity of a Non-KAM System Through Out-of-Time-Order Correlators
- Scaling at the OTOC Wavefront: free versus chaotic models
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