MCS-MP Seminar: Sebastien Breteaux

Speaker: Sébastien Breteaux (Lorraine)

Title: Exponential Decay outside of the Light Cone for the Pseudo-Relativistic Non-Autonomous Schrödinger Equation

Abstract: We establish a maximal velocity bound for a pseudo-relativistic quantum particle in an external time-dependent potential. Our estimate shows that the probability for the particle, starting in a convex set $X \subset \mathbb{R}^d$ at $t=0$, to reach a convex set $Y \subset \mathbb{R}^d$ at a positive time $t$, is bounded by $\exp(-2r)$ where $r$ is the distance from $Y$ to the section at time $t$ of the light cone generated by $X$.