Quantum vortices and trajectories in particle diffraction

TL;DR

This paper explores how quantum vortices influence particle trajectories during diffraction, using de Broglie-Bohm theory, revealing vortex structures and proposing experimental tests for quantum trajectory behavior.

Contribution

It introduces a detailed analysis of quantum vortices and their impact on diffraction patterns within the de Broglie-Bohm framework, including new scaling laws and trajectory deflection mechanisms.

Findings

Identification of quantum vortex structures near the diffraction separator

Demonstration of vortex influence on particle trajectory deflections

Proposal of experimental tests based on particle times of flight

Abstract

We investigate the phenomenon of the diffraction of charged particles by thin material targets using the method of the de Broglie-Bohm quantum trajectories. The particle wave function can be modeled as a sum of two terms $\psi=\psi_{ingoing}+\psi_{outgoing}$. A thin separator exists between the domains of prevalence of the ingoing and outgoing wavefunction terms. The structure of the quantum-mechanical currents in the neighborhood of the separator implies the formation of an array of \emph{quantum vortices}. The flow structure around each vortex displays a characteristic pattern called `nodal point - X point complex'. The X point gives rise to stable and unstable manifolds. We find the scaling laws characterizing a nodal point-X point complex by a local perturbation theory around the nodal point. We then analyze the dynamical role of vortices in the emergence of the diffraction pattern. In particular, we demonstrate the abrupt deflections, along the direction of the unstable manifold, of the quantum trajectories approaching an X-point along its stable manifold. Theoretical results are compared to numerical simulations of quantum trajectories. We finally calculate the {\it times of flight} of particles following quantum trajectories from the source to detectors placed at various scattering angles $\theta$, and thereby propose an experimental test of the de Broglie - Bohm formalism.