WKB analysis of Bohmian dynamics

TL;DR

This paper analyzes the behavior of Bohmian trajectories in the semiclassical limit, showing convergence to classical trajectories before caustic formation and divergence afterward, supported by numerical simulations.

Contribution

It provides a rigorous analysis of Bohmian dynamics in the semiclassical regime, highlighting the limits of classical convergence before caustic onset.

Findings

Bohmian trajectories converge to classical ones before caustics

Convergence fails after caustic formation

Numerical simulations illustrate theoretical results

Abstract

We consider a semi-classically scaled Schr\"odinger equation with WKB initial data. We prove that in the classical limit the corresponding Bohmian trajectories converge (locally in measure) to the classical trajectories before the appearance of the first caustic. In a second step we show that after caustic onset this convergence in general no longer holds. In addition, we provide numerical simulations of the Bohmian trajectories in the semiclassical regime which illustrate the above results.