Semiclassical time evolution and quantum ergodicity for Dirac-Hamiltonians

TL;DR

This paper establishes a quantum-classical correspondence for Dirac-Hamiltonians using Weyl calculus, including a semiclassical separation of particles and antiparticles, and proves quantum ergodicity under certain classical ergodic conditions.

Contribution

It introduces a novel semiclassical analysis for Dirac-Hamiltonians and proves quantum ergodicity based on classical ergodic properties of combined relativistic motion and spin precession.

Findings

Quantum-classical correspondence for Dirac-Hamiltonians established.

Semiclassical separation of particles and antiparticles demonstrated.

Quantum ergodicity proven under classical ergodic conditions.

Abstract

Within the framework of Weyl calculus we establish a quantum-classical correspondence for the time evolution of observables generated by a Dirac-Hamiltonian. This includes a semiclassical separation of particles and antiparticles. We then prove quantum ergodicity for Dirac-Hamiltonians under the condition that a skew product of the classical relativistic translational motion and relativistic spin precession is ergodic.