A one-dimensional lattice model for a quantum mechanical free particle

TL;DR

This paper introduces a one-dimensional lattice model with two particle types whose interactions replicate the quantum mechanical behavior of a free particle over time.

Contribution

It presents a novel lattice model where particle interactions produce quantum free particle dynamics, bridging classical lattice systems and quantum mechanics.

Findings

Particles' distribution follows quantum free particle evolution

Nonlocal interactions decrease with distance

Model reproduces quantum mechanical time evolution

Abstract

Two types of particles, A and B with their corresponding antiparticles, are defined in a one dimensional cyclic lattice with an odd number of sites. In each step of time evolution, each particle acts as a source for the polarization field of the other type of particle with nonlocal action but with an effect decreasing with the distance: A -->...\bar{B} B \bar{B} B \bar{B} ... ; B --> A \bar{A} A \bar{A} A ... . It is shown that the combined distribution of these particles obeys the time evolution of a free particle as given by quantum mechanics.