Quantum chaos using the delta kicked accelerator

The quantum delta kicked accelerator (QAM) can be realized by subjecting a particle to a periodic $\delta$-potential and a linear potential such as gravity. The quantum $\delta$-kicked accelerator exhibits a phenomenon of resonance which happens whenever the period of kicking is a rational fraction of the half-Talbot time. A theory of QAM occurring at integer multiples of the half-Talbot time was developed by [1] which treats the closeness of the time period to one of the primary resonance as Planck's constant and a classical mapping can be used to study the resonances. Here we extend the $\epsilon$-classical theory to the resonances occurring at high order resonances and use the classical mapping to study these resonances. [1] S. Fishman et. al., Phys. Rev. Lett. 89, 084101 (2002); J. Stat. Phys. 110, 911 (2003).