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 make the adiabatic evolution 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.

6 pages, 2 figures

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Cited by in corpus (4)

• Landau-Zener Tunnelling in a Nonlinear Three-level System
• Nonlinear Ramsey interferometry with the Rosen-Zener pulses on a two-component Bose-Einstein condensate
• Rosen-Zener interferometry with Ultracold Atoms
• Quantum Hamiltonian daemons: unitary analogs of combustion engines