KAM-Stability for Conserved Quantities in Finite-Dimensional Quantum Systems
Quantum Physics
2021-04-14 v2
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.
Cite
@article{arxiv.2011.04707,
title = {KAM-Stability for Conserved Quantities in Finite-Dimensional Quantum Systems},
author = {Daniel Burgarth and Paolo Facchi and Hiromichi Nakazato and Saverio Pascazio and Kazuya Yuasa},
journal= {arXiv preprint arXiv:2011.04707},
year = {2021}
}
Comments
13 pages, 3 figures. Corrected typo in author name and added arXiv link to reference [16]