Quantum ergodicity for Pauli Hamiltonians with spin 1/2

TL;DR

This paper proves quantum ergodicity for spin 1/2 particles, showing that eigenstate expectation values converge to classical averages when combined classical and spin dynamics are ergodic.

Contribution

It establishes quantum ergodicity for systems with spin 1/2, extending previous results to include spin dynamics in the ergodic framework.

Findings

Quantum ergodicity holds for particles with spin 1/2.

Convergence of expectation values to classical averages is proven.

Ergodicity of combined translational and spin dynamics is key.

Abstract

Quantum ergodicity, which expresses the semiclassical convergence of almost all expectation values of observables in eigenstates of the quantum Hamiltonian to the corresponding classical microcanonical average, is proven for non-relativistic quantum particles with spin 1/2. It is shown that quantum ergodicity holds, if a suitable combination of the classical translational dynamics and the spin dynamics along the trajectories of the translational motion is ergodic.