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We investigate the classical chaotic diffusion of atoms subjected to {\empairs} of closely spaced pulses (`kicks) from standing waves of light (the$2\delta$-KP). Recent experimental studies with cold atoms implied anunderlying classical diffusion of type very different from the well-knownparadigm of Hamiltonian chaos, the Standard Map.  The kicks in each pair are separated by a small time interval $\epsilon \ll1$, which together with the kick strength $K$, characterizes the transport.Phase space for the $2\delta$-KP is partitioned into momentum `cells' partiallyseparated by momentum-trapping regions where diffusion is slow. We present herean analytical derivation of the classical diffusion for a $2\delta$-KPincluding all important correlations which were used to analyze theexperimental data.  We find a new asymptotic ($t \to \infty$) regime of `hindered' diffusion:while for the Standard Map the diffusion rate, for $K \gg 1$, $D \sim K^2/2[1-J_2(K)..]$ oscillates about the uncorrelated, rate $D_0 =K^2/2$, we findanalytically, that the $2\delta$-KP can equal, but never diffuses faster than,a random walk rate.  We argue this is due to the destruction of the important classical`accelerator modes' of the Standard Map.  We analyze the experimental regime $0.1\lesssim K\epsilon \lesssim 1$, wherequantum localisation lengths $L \sim \hbar^{-0.75}$ are affected by fractalcell boundaries. We find an approximate asymptotic diffusion rate $D\proptoK^3\epsilon$, in correspondence to a $D\propto K^3$ regime in the Standard Mapassociated with 'golden-ratio' cantori.Comment: 14 pages, 10 figures, error in equation in appendix correcte

physical review. e, statistical, nonlinear and soft matter physics

Classical momentum diffusion in double-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>δ</mml:mi></mml:math>-kicked particles

Classical momentum diffusion in double-δ-kicked particles