Current-based Simulation Models of Quantum Motion

TL;DR

This paper introduces a classical simulation model for quantum particle motion based on current-based diffusion, reproducing key quantum phenomena like wave-particle duality, energy quantization, and interference patterns.

Contribution

It develops a classical, current-based diffusion model that replicates quantum trajectories, Born's rule, and interference effects, offering a new perspective on quantum simulation.

Findings

Reproduces Talbot patterns and distances for multi-slit systems

Derives a ballistic diffusion equation for particle trajectories

Explains the sweeper effect in double-slit experiments

Abstract

With purely classical tools a model for a bouncer-walker system of an elementary particle will be derived in this work which reflects the old idea of de Broglie's particle-wave duality. This model contains, on the one hand, a possible explanation of the work-energy exchange between the two separated motions, thereby providing an energy quantisation as originally postulated by Max Planck. On the other hand, the system perfectly obeys the Bohmian-type law of motion in full accordance with quantum mechanics. For the calculation of elementary particles' trajectories a ballistic diffusion equation will be derived which is a special case of a diffusion equation with a time-dependent diffusivity. Therewith the simulation of spreading of an elementary Gaussian is made easy as will be shown herein. With these tools one also accounts for Born's rule for multi-slit systems and develops a set of current rules that directly leads to a new formulation of the guiding equation equivalent to the original one of the de Broglie-Bohm theory. As will be shown in this thesis, this tool reproduces Talbot patterns and Talbot distance for an arbitrary multi-slit system. Moreover, the sweeper effect is shown to arise when the intensity relation of two beams of a double-slit experiment exhibit a big difference. Then, the low-intensity beam is pushed aside in a sense that its initial propagation straight out of the slit is bent towards the side. A sideways screen as an alternative measurement method is proposed.