Changes in Floquet state structure at avoided crossings: delocalization   and harmonic generation
  Avoided crossings are common in the quasienergy spectra of strongly driven nonlinear quantum wells. In this paper we examine the sinusoidally driven particle in a square potential well to show that avoided crossings can alter the structure of Floquet states in this system. Two types of avoided crossings are identified: on type leads only to temporary changes (as a function of driving field strength) in Floquet state structure while the second type can lead to permanent delocalization of the Floquet states. Radiation spectra from these latter states show significant increase in high harmonic generation as the system passes through the avoided crossing. 
T. Timberlake and L. E. Reichl