Wavepacket approach to particle diffraction by thin targets: Quantum trajectories and arrival times

TL;DR

This paper develops a wavepacket approach combined with de Broglie-Bohm trajectories to analyze particle diffraction by thin targets, revealing quantum vortex structures, diffraction patterns, and differences in arrival time predictions compared to other theories.

Contribution

It introduces a novel wavepacket and trajectory-based framework for understanding particle diffraction, including the formation of quantum vortices and a new perspective on arrival times.

Findings

Quantum vortices form near the separator in diffraction.

Deformation of the separator explains diffraction patterns.

Predicted arrival times differ from other quantum theories.

Abstract

We develop a wavepacket approach to the diffraction of charged particles by a thin material target and we use the de Broglie-Bohm quantum trajectories to study various phenomena in this context. We find the form of the separator, i.e.the limit between the domains of prevalence of the ingoing and outgoing quantum flow. The structure of the quantum-mechanical currents in the neighborhood of the separator implies the formation of an array of \emph{quantum vortices} (nodal point - X point complexes). We show how the deformation of the separatior near Bragg angles explains the emergence of a diffraction pattern by the de Broglie - Bohm trajectories. We calculate the arrival time distributions for particles scattered at different angles. The predictions of the de Broglie - Bohm theory for $\Delta T$ turn to be different from estimates of the same quantity using other theories on time observables like the sum-over-histories or the Kijowski approach. We propose an experimental setup aiming to test such predictions. Finally, we explore the semiclassical limit of short wavelength and short quantum coherence lengths, and demonstrate how, in this case, results with the de Broglie - Bohm trajectories are similar to the classical results of Rutherford scattering.