N-Slit Interference: Fractals in Near-Field Region, Bohmian Trajectories

TL;DR

This paper demonstrates how cold particles scattering on an N-slit grating produce near-field fractal interference patterns and analyzes particle trajectories using Bohmian mechanics, linking near-field fractals to far-field diffraction.

Contribution

It introduces a detailed analysis of N-slit interference patterns, including fractal Talbot carpets and Bohmian trajectories, bridging near-field fractals with far-field diffraction.

Findings

Near-field interference forms fractal Talbot carpets.

Bohmian trajectories pass through only one slit.

Far-field pattern shows principal and weak beams.

Abstract

Scattering cold particles on an $N$-slit grating is shown to reproduce an interference pattern, that manifests itself in the near-field region as the fractal Talbot carpet. In the far-field region the pattern is transformed to an ordinary diffraction, where principal beams are partitioned from each other by ($N-2$) weak ones. A probability density plot of the wave function, to be represented by a gaussian wavepacket, is calculated both in the near-field region and in the far-field one. Bohmian (geodesic) trajectories, to be calculated by a guidance equation, are superimposed on the probability density plot well enough. It means, that a particle, moving from a source to a detector, passes across the grating along a single bohmian trajectory through-passing one and only one slit. Keywords: Gaussian wavepacket, neutron scattering, guidance equation, bohmian trajectory, near-field interference, far-field diffraction, Talbot carpet, fractal