Confining massless Dirac particles in two-dimensional curved space

TL;DR

This paper demonstrates that curvature in two-dimensional space can confine massless Dirac particles, using a quantum lattice Boltzmann method to solve the Dirac equation in curved geometries.

Contribution

It introduces a novel numerical approach to simulate Dirac particles in curved space and quantifies confinement probability based on spatial curvature.

Findings

Curvature can confine a portion of a massless Dirac wave-packet.

A power law relates confinement probability to average spatial curvature.

The method enables studying Dirac particles in curved geometries.

Abstract

Dirac particles have been notoriously difficult to confine. Implementing a curved space Dirac equation solver based on the quantum Lattice Boltzmann method, we show that curvature in a 2-D space can confine a portion of a charged, mass-less Dirac fermion wave-packet. This is equivalent to a finite probability of confining the Dirac fermion within a curved space region. We propose a general power law expression for the probability of confinement with respect to average spatial curvature for the studied geometry.