Localized shocks

We study products of precursors of spatially local operators, , where W (x) (t) = e (-aEuro parts per thousand 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.