PT - JOURNAL ARTICLE
AU -
AU -
TI - The geometric phase for chaotic systems
DP - 1992 Mar 09
TA - Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences
PG - 631--661
VI - 436
IP - 1898
4099 - http://rspa.royalsocietypublishing.org/content/436/1898/631.short
4100 - http://rspa.royalsocietypublishing.org/content/436/1898/631.full
AB - The geometric phase acquired by the eigenstates of cycled quantum systems is given by the flux of a two-form through a surface in the systemâ€™s parameter space. We obtain the classical limit of this two-form in a form applicable to systems whose classical dynamics is chaotic. For integrable systems the expression is equivalent to the Hannay two-form. We discuss various properties of the classical two-form, derive semiclassical corrections to it (associated with classical periodic orbits), and consider implications for the semiclassical density of degeneracies.