Modeling double slit interference via anomalous diffusion: independently variable slit widths

TL;DR

This paper introduces a novel simulation method for double-slit interference using anomalous diffusion, accurately reproducing quantum intensity and trajectory distributions with a local phase approach, based on a re-formulation of classical Gaussian dispersion.

Contribution

It presents a practical simulation framework connecting anomalous sub-quantum diffusion to quantum interference, enabling precise modeling of phase, intensity, and current distributions for variable slit widths.

Findings

Successfully reproduces quantum intensity distributions

Accurately models trajectory and current distributions

Handles phase shifts affecting single slits

Abstract

Based on a re-formulation of the classical explanation of quantum mechanical Gaussian dispersion (Groessing et al. 2010) as well as interference of two Gaussians (Groessing et al. 2012), we present a new and more practical way of their simulation. The quantum mechanical "decay of the wave packet" can be described by anomalous sub-quantum diffusion with a specific diffusivity varying in time due to a particle's changing thermal environment. In a simulation of the double-slit experiment with different slit widths, the phase with this new approach can be implemented as a local quantity. We describe the conditions of the diffusivity and, by connecting to wave mechanics, we compute the exact quantum mechanical intensity distributions, as well as the corresponding trajectory distributions according to the velocity field of two Gaussian wave packets emerging from a double-slit. We also calculate probability density current distributions, including situations where phase shifters affect a single slit's current, and provide computer simulations thereof.