Maximal Speed of Quantum Propagation for the Hartree equation
Analysis of PDEs
2023-02-22 v1 Mathematical Physics
math.MP
Abstract
We prove maximal speed estimates for nonlinear quantum propagation in the context of the Hartree equation. More precisely, under some regularity and integrability assumptions on the pair (convolution) potential, we construct a set of energy and space localized initial conditions such that, up to time-decaying tails, solutions starting in this set stay within the light cone of the corresponding initial datum. We quantify precisely the light cone speed, and hence the speed of nonlinear propagation, in terms of the momentum of the initial state.
Keywords
Cite
@article{arxiv.2302.10519,
title = {Maximal Speed of Quantum Propagation for the Hartree equation},
author = {Jack Arbunich and Jérémy Faupin and Fabio Pusateri and Israel Michael Sigal},
journal= {arXiv preprint arXiv:2302.10519},
year = {2023}
}
Comments
38 pages. Appendices D and E are adapted from arXiv:2011.04570. To appear in Communications in Partial Differential Equations