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The effect of pulse train noise on the quantum resonance peaks of the AtomOptics Kicked Rotor is investigated experimentally. Quantum resonance peaks inthe late time mean energy of the atoms are found to be surprisingly robustagainst all levels of noise applied to the kicking amplitude, whilst even smalllevels of noise on the kicking period lead to their destruction. The robustnessto amplitude noise of the resonance peak and of the fall--off in mean energy toeither side of this peak are explained in terms of the occurence of stable,$\epsilon$--classical dynamics [S. Wimberger, I. Guarneri, and S. Fishman,\textit{Nonlin.} \textbf{16}, 1381 (2003)] around each quantum resonance.Comment: 9 pages, four figure

Observation of robust quantum resonance peaks in an atom optics kicked rotor with amplitude noise