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Generation and Coherent Control of Pulsed Quantum Frequency Combs
Published on: June 8, 2018
Kolmogorov-Arnold-Moser Stability for Conserved Quantities in Finite-Dimensional Quantum Systems
Daniel Burgarth1, Paolo Facchi2,3, Hiromichi Nakazato4
1Center for Engineered Quantum Systems, Department of Physics and Astronomy, Macquarie University, 2109 New South Wales, Australia.
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 theorem in classical mechanics. To prove this result, we introduce a resummation of a perturbation series, which generalizes the Hamiltonian of the quantum Zeno dynamics.
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