[2607.14220] Non-perturbative saturation of Krylov complexity, and its implications in quantum gravity

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Summary:We examine the dynamics of Krylov state complexity in finite-dimensional quantum methods. Orthogonal polynomials constructed on a discrete vitality spectrum crowd away from areas the place the density of states is low at giant Krylov index. The bodily implication of this result’s that, even utilizing a minimalist Krylov state complexity which is outlined over the whole spectrum, the Krylov complexity provably stops rising a bit previous the Heisenberg size in each low-energy state. This has fascinating implications for the proposal that Krylov complexity is expounded to the wormhole size in 2D quantum gravity.