Semiclassics for particles with spin via a Wigner-Weyl-type calculus
Mathematical Physics
2015-03-13 v1 math.MP
Abstract
We show how to relate the full quantum dynamics of a spin-1/2 particle on R^d to a classical Hamiltonian dynamics on the enlarged phase space R^d x S^2 up to errors of second order in the semiclassical parameter. This is done via an Egorov-type theorem for normal Wigner-Weyl calculus for R^d [Lei10,Fol89] combined with the Stratonovich-Weyl calculus for SU(2) [VGB89]. For a specific class of Hamiltonians, including the Rabi- and Jaynes-Cummings model, we prove an Egorov theorem for times much longer than the semiclassical time scale. We illustrate the approach for a simple model of the Stern-Gerlach experiment.
Cite
@article{arxiv.1307.8068,
title = {Semiclassics for particles with spin via a Wigner-Weyl-type calculus},
author = {Omri Gat and Max Lein and Stefan Teufel},
journal= {arXiv preprint arXiv:1307.8068},
year = {2015}
}
Comments
24 pages