Divergences in the iterative and perturbative methods for computing Hannays angle

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Abstract

A classical analog is obtained for Berrys nonperturbative scheme of adiabatic iteration which computes corrections to Berrys phase (or Hannays angle) for finite values of the adiabatic parameter . The iterative method is compared to the Lie version of adiabatic perturbation theory. Both approaches show a divergence of k!k, where k is the order of iteration. It is argued that the divergences are a mathematical artifact of the asymptotic methods used, not related to the physical effect of transitions, nor to the nonconservation of the action variables.

Original languageEnglish (US)
Pages (from-to)5650-5665
Number of pages16
JournalPhysical Review A
Volume41
Issue number10
DOIs
StatePublished - Jan 1 1990
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Atomic and Molecular Physics, and Optics

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