Light cones for open quantum systems

09/06/2023 4:00 pm - 5:00 pm
Science Center 232
Address: Harvard Science Center, 1 Oxford Street, Cambridge MA 02138

Probability Seminar

Speaker: Marius Lemm, University of Tuebingen

Title: Light cones for open quantum systems
Abstract: We consider non-relativistic Markovian open quantum dynamics in continuous space. We show that, up to small probability tails, the supports of quantum states propagate with finite speed in any finite-energy subspace. More precisely, 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 on the slope of this light cone (i.e., on the maximal speed). The general method can be used to derive propagation bounds for a variety of other quantum systems including Lieb-Robinson bounds for lattice bosons. Based on joint works with S. Breteaux, J. Faupin, D.H. Ou Yang, I.M. Sigal, and J. Zhang.