Modelling quantum mechanical double slit interference via anomalous diffusion: Independently variable slit widths

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.

The article was published in: Physica A: Statistical Mechanics and its Applications 392(12): 2718-2727.

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This work was supported (in part) by the Fetzer Franklin Fund of the John E. Fetzer Memorial Trust.