2019
DOI: 10.22331/q-2019-06-12-152
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Generalized Adiabatic Theorem and Strong-Coupling Limits

Abstract: 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 52 publications
(68 citation statements)
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“…The third and ultimate ingredient is a strong-coupling theorem developed by the present authors recently in Ref. [11] (see also Ref. [12]), which can be applied to unphysical generators (Theorem 1 of Ref.…”
Section: Introductionmentioning
confidence: 99%
See 1 more Smart Citation
“…The third and ultimate ingredient is a strong-coupling theorem developed by the present authors recently in Ref. [11] (see also Ref. [12]), which can be applied to unphysical generators (Theorem 1 of Ref.…”
Section: Introductionmentioning
confidence: 99%
“…[12]), which can be applied to unphysical generators (Theorem 1 of Ref. [11]). Even though the logarithm of a physical operation is not of the GKLS form in general, one can deal with it by the adiabatic theorem proved in Ref.…”
Section: Introductionmentioning
confidence: 99%
“…Clearly, there are many more choices and depending on L and P , these may or may not generate a completely positive evolution on T (H). For a particular example see [11] (remark 4, example 1).…”
Section: Time-independent Casementioning
confidence: 99%
“…The literature on the quantum Zeno effect is vast (see [6,7] for an overview) and we can only mention those works that appear to be closest to ours. For finite-dimensional quantum systems with time-independent evolution equations the quantum Zeno effect has been generalized towards more general measurements for Hamiltonian dynamcis in [8,9,10] and for Lindblad-type dynamics, in parallel to the present work, in [11,12]. [12] also allow for finite families of arbitrary quantum operations and in this way follow an interesting route that is not addressed in the present paper.…”
Section: Introductionmentioning
confidence: 99%
“…This is only a part of the whole picture. Most results can be generalized to master (GKLS [26]) equations, quantum semigroups, and sequences of generic quantum operations [27][28][29][30]. Moreover, the analysis can be extended to multidimensional spaces, highlighting interesting relations with geometry [31,32] and complexity [33].…”
Section: Comments and Conclusionmentioning
confidence: 99%