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Krylov complexity, path integrals, and instantons

2025/07/17 by Cameron Beetar, Beetar, Cameron, Eric L Graef +7 · 1 citation
Computer Science · Mathematics · #Cellular Automata and Applications #FOS: Physical sciences #Graph theory and applications #High Energy Physics - Theory (hep-th) #Quantum Physics (quant-ph) #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.2507.13226

openalex publication_date 2025/07/17 · openalex created_date 2025/10/18 · openalex updated_date 2026/07/28

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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