Localized shocks

We study products of precursors of spatially local operators, Wₓₙ (tn) Wₗ䃑 (t₁), where W x (t) = e − iHt W x e iHt. Using chaotic spin-chain numerics and gauge/gravity duality, we show that a single precursor fills a spatial region that grows linearly in t. In a lattice system, products of such operators can be represented using tensor networks. In gauge/gravity duality, they are related to Einstein-Rosen bridges supported by localized shock waves. We find a geometrical correspondence between these two descriptions, generalizing earlier work in the spatially homogeneous case.