Dynamic diffusion as approximation of quantum behavior

TL;DR

This paper introduces a classical swarm-based approximation of quantum dynamics that uses creation and annihilation of bonds to simulate quantum behavior, enabling scalable modeling of many particles including entangled states.

Contribution

It presents a novel method that approximates quantum unitary dynamics through a swarm of classical samples with bond mechanisms, avoiding density differentiation and allowing for scalable multi-particle simulations.

Findings

Method effectively approximates quantum probability densities.

Applicable to entangled multi-particle states.

Models decoherence through bond dynamics.

Abstract

The approximation of quantum unitary dynamics of a particle by a swarm of point wise classical samples of this particle is proposed. Quantum mechanism of speedup rests on the creation and annihilation of absolutely rigid bons, which join samples in dot wise symplexes so that the density of swarm approximate the quantum probability. This mechanism does not require differentiation of a density that is adventage of this method over Bohm's quantum hydrodynamics: our method is applicable to many particles in entangled states. In multi particle case the limitation of total number of samples gives the natural model of decoherence, e.g. the divergency from the exact solution of Shredinger equation. Intensity of creation - annihilation of bonds between samples substantially depends on the grain of spatial resolution, which makes impossible to pass to the limits as in a classical substance; this is the price for the scalability of a model to many particles.