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29 March 2024
 
  » arxiv » 1307.8068

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Semiclassics for particles with spin via a Wigner-Weyl-type calculus
Omri Gat ; Max Lein ; Stefan Teufel ;
Date 30 Jul 2013
AbstractWe 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.
Source arXiv, 1307.8068
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