Semiclassical propagation of coherent states with spin-orbit interaction

TL;DR

This paper develops semiclassical methods to approximate the quantum evolution of coherent states in spin-orbit systems, analyzing different classical limits and improving approximation accuracy over time.

Contribution

It introduces a framework for semiclassical propagation of coherent states with spin-orbit interaction, identifying classical dynamics and error bounds in different regimes.

Findings

Quantum evolution approximated by classical dynamics up to t error

Different classical spin-orbit dynamics emerge in two semiclassical limits

Error can be reduced to arbitrary order a7h^{N/2} with state deformation

Abstract

We study semiclassical approximations to the time evolution of coherent states for general spin-orbit coupling problems in two different semiclassical scenarios: The limit \hbar to zero is first taken with fixed spin quantum number s and then with \hbar*s held constant. In these two cases different classical spin-orbit dynamics emerge. We prove that a coherent state propagated with a suitable classical dynamics approximates the quantum time evolution up to an error of size \sqrt{\hbar} and identify an Ehrenfest time scale. Subsequently an improvement of the semiclassical error to an arbitray order \hbar^{N/2} is achieved by a suitable deformation of the state that is propagated classically.