Krylov complexity, path integrals, and instantons
Krylov complexity, path integrals, and instantons
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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