The group velocity and Lieb-Robinson velocity of a periodic Schrodinger operator decay as mu^{-p0+1} in the large-coupling limit, where p0 is the minimal period.
Light cones for open quantum systems
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We consider Markovian open quantum dynamics (MOQD). We show that, up to small-probability tails, the supports of quantum states evolving under such dynamics propagate with finite speed in any finite-energy subspace. More precisely, we prove that if the initial quantum state is localized in space, then any finite-energy part of the solution of the von Neumann-Lindblad equation is approximately localized inside an energy-dependent light cone. We also obtain an explicit upper bound for the slope of this light cone.
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Sharp Polynomial Velocity Decay Bounds for Multidimensional Periodic Schr\"odinger Operators
The group velocity and Lieb-Robinson velocity of a periodic Schrodinger operator decay as mu^{-p0+1} in the large-coupling limit, where p0 is the minimal period.