Kolmogorov-Arnold-Moser Stability for Conserved Quantities in Finite-Dimensional Quantum Systems

Daniel Burgarth, Paolo Facchi, Hiromichi Nakazato, Saverio Pascazio, Kazuya Yuasa

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Article number150401
JournalPhysical Review Letters
Volume126
Issue number15
DOIs
Publication statusPublished - 2021 Apr 12

ASJC Scopus subject areas

  • Physics and Astronomy(all)

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