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
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.