title: Topology hidden behind the breakdown of adiabaticity.
abstract: For classical Hamiltonian systems, the adiabatic condition may fail at some critical points. However, the breakdown of the adiabatic condition does not always cause the adiabatic evolution to be destroyed. In this paper, we suggest a supplemental condition of the adiabatic evolution for the fixed points of classical Hamiltonian systems when the adiabatic condition breaks down at the critical points. As an example, we investigate the adiabatic evolution of the fixed points of a classical Hamiltonian system which has a number of applications.
authors.affiliation: Institute of Applied Physics and Computational Mathematics, P.O. Box 8009 (28), 100088 Beijing, China.
authors.forename: Li-Bin
authors.initials: LB
authors.lastname: Fu
authors.forename: Shi-Gang
authors.initials: SG
authors.lastname: Chen