Creation Rate of Dirac Particles at a Point Source

TL;DR

This paper develops a Bohmian mechanics-based Markov jump process for Dirac particles created at a point source, analyzing the particle dynamics and creation rates in a rigorous quantum framework.

Contribution

It introduces a new Bohmian configuration process for Dirac particles with point-source creation, including the derivation of creation rates and trajectory behavior.

Findings

Particles reach the source with zero radial speed.

Particles orbit the source infinitely many times in finite time.

The process models particle creation and annihilation events accurately.

Abstract

Only recently has it been possible to construct a self-adjoint Hamiltonian that involves the creation of Dirac particles at a point source in 3d space. Its definition makes use of an interior-boundary condition. Here, we develop for this Hamiltonian a corresponding theory of the Bohmian configuration. That is, we construct a Markov jump process $(Q_t)_{t\in\mathbb{R}}$ in the configuration space of a variable number of particles that is $|\psi_t|^2$-distributed at every time $t$ and follows Bohmian trajectories between the jumps. The jumps correspond to particle creation or annihilation events and occur either to or from a configuration with a particle located at the source. The process is the natural analog of Bell's jump process, and a central piece in its construction is the determination of the rate of particle creation. The construction requires an analysis of the asymptotic behavior of the Bohmian trajectories near the source. We find that the particle reaches the source with radial speed 0, but orbits around the source infinitely many times in finite time before absorption (or after emission).