Quantum statistical effects in one-particle densities: scattering and pair production

TL;DR

This paper investigates how external fields produce particle-hole pairs in quantum systems, revealing that in some cases, densities depend solely on initial states and are unaffected by quantum statistics, with extensions to relativistic particles.

Contribution

It extends second quantisation techniques to Dirac electrons and Klein-Gordon bosons, analyzing differences in pair production between relativistic cases.

Findings

Densities can be independent of Fermi-Dirac or Bose-Einstein statistics.

Extension of second quantisation to relativistic particles.

Analysis of pair production differences in relativistic regimes.

Abstract

We study space-time resolved densities of particle-hole pairs produced by an external time-dependent field acting on non-interacting non-relativistic particles. It is shown that, at least in some cases, the densities are not affected by Fermi-Dirac or Bose- Einstein statistics, and are determined only by the initial state of the multi-particle system. The second quantisation technique is extended to Dirac electrons and, with some modifications, to Klein-Gordon bosons. The difference in pair production in these two relativistic cases is analysed in some detail.