Abstract
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 system’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.
Reference30 articles.
1. Abraham R. & Marsden J. E. 1978 Foundations of mechanics p. 461. Reading: Benjamin-Cummings.
2. Arnold V. I. 1978 Mathematical methods of classical mechanics. New York: Springer.
3. Arnold V. I. & Avez A. 1989 Ergodic problems of classical mechanics. Redwood City: Addison-Wesley.
4. Communs math;Avron J. E.;Phys.,1987
5. Rev. mod;Avron J. E.;Phys.,1988
Cited by
32 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献