Bohm - de Broglie Cycles

TL;DR

This paper investigates the trajectories of relativistic spin-one-half particles in the de Broglie-Bohm theory, revealing circular to linear motion transitions and calculating arrival time distributions relevant to graphene physics.

Contribution

It provides explicit numerical analysis of particle trajectories in relativistic quantum theory, focusing on massless particles with angular momentum eigenstates.

Findings

Trajectories transition from circles to straight lines.

Arrival time distributions are computed.

Results are relevant to graphene physics.

Abstract

In the de Broglie-Bohm quantum theory, particles describe trajectories determined by the flux associated with their wave function. These trajectories are studied here for relativistic spin-one-half particles.Based in explicit numerical calculations for the case of a massless particle in dimension three space-time, it is shown that if the wave function is an eigenfunction of the total angular momentum, the trajectories begin as circles of slowly increasing radius until a transition time at which they tend to follow straight lines. Arrival times at some detector, as well as their probability distribution are calculated, too. The chosen energy and momentum parameters are of the orders of magnitude met in graphene's physics.