Generalized Adiabatic Theorem and Strong-Coupling Limits

Daniel Burgarth1, Paolo Facchi2,3, Hiromichi Nakazato4, Saverio Pascazio2,3,5, and Kazuya Yuasa4

1Center for Engineered Quantum Systems, Dept. of Physics & Astronomy, Macquarie University, 2109 NSW, Australia
2Dipartimento di Fisica and MECENAS, Università di Bari, I-70126 Bari, Italy
3INFN, Sezione di Bari, I-70126 Bari, Italy
4Department of Physics, Waseda University, Tokyo 169-8555, Japan
5Istituto Nazionale di Ottica (INO-CNR), I-50125 Firenze, Italy

We generalize Kato's adiabatic theorem to nonunitary dynamics with an isospectral generator. This enables us to unify two strong-coupling limits: one driven by fast oscillations under a Hamiltonian, and the other driven by strong damping under a Lindbladian. We discuss the case where both mechanisms are present and provide nonperturbative error bounds. We also analyze the links with the quantum Zeno effect and dynamics.

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Cited by

[1] Tim Möbus and Michael M. Wolf, "Quantum Zeno effect generalized", Journal of Mathematical Physics 60 5, 052201 (2019).

[2] Paolo Facchi and Saverio Pascazio, "Kick and fix: the roots of quantum control", arXiv:1902.01591.

[3] Daniel Burgarth, Paolo Facchi, Hiromichi Nakazato, Saverio Pascazio, and Kazuya Yuasa, "Quantum Zeno Dynamics from General Quantum Operations", arXiv:1809.09570.

[4] Norbert Barankai and Zoltán Zimborás, "Generalized quantum Zeno dynamics and ergodic means", arXiv:1811.02509.

[5] Daniel Burgarth, Paolo Facchi, Giovanni Gramegna, and Saverio Pascazio, "Generalized Product Formulas and Quantum Control", arXiv:1906.04498.

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