Maximal Speed of Quantum Propagation for the Hartree equation

TL;DR

This paper establishes bounds on the maximum speed of quantum information propagation in the Hartree equation, linking it to initial momentum and providing precise light cone speed estimates.

Contribution

It introduces maximal speed estimates for nonlinear quantum propagation in the Hartree equation, relating propagation speed to initial data momentum.

Findings

Solutions remain within a light cone up to decaying tails.

Propagation speed is quantitatively linked to initial momentum.

The paper provides explicit bounds on the speed of nonlinear quantum propagation.

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.