Krylov complexity, path integrals, and instantons

• URL: http://arxiv.org/abs/2507.13226v1
• Date: Thu, 17 Jul 2025 15:38:59 GMT
• Title: Krylov complexity, path integrals, and instantons
• Authors: Cameron Beetar, Eric L Graef, Jeff Murugan, Horatiu Nastase, Hendrik J R Van Zyl,
• Abstract summary: We formulate Krylov complexity $K(t)$ for quantum mechanical systems as a path integral.<n>We 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.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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