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Krylov complexity, path integrals, and instantons

Krylov complexity, path integrals, and instantons

来源:Arxiv_logoArxiv
英文摘要

Krylov complexity has emerged as an important tool in the description of quantum information and, in particular, quantum chaos. Here we formulate Krylov complexity $K(t)$ for quantum mechanical systems as a path integral, and argue that at large times, for classical chaotic systems with at least two minima of the potential, that have a plateau for $K(t)$, the value of the plateau is described by quantum mechanical instantons, as is the case for standard transition amplitudes. We explain and test these ideas in a simple toy model.

Cameron Beetar、Eric L Graef、Jeff Murugan、Horatiu Nastase、Hendrik J R Van Zyl

物理学

Cameron Beetar,Eric L Graef,Jeff Murugan,Horatiu Nastase,Hendrik J R Van Zyl.Krylov complexity, path integrals, and instantons[EB/OL].(2025-07-17)[2025-08-18].https://arxiv.org/abs/2507.13226.点此复制

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