dorsal/arxiv
View SchemaClassical diffusion in double-delta-kicked particles
| Authors | M. M. A. Stocklin, T. S. Monteiro |
|---|---|
| Categories | |
| ArXiv ID | physics/0408088 |
| URL | https://arxiv.org/abs/physics/0408088 |
| DOI | 10.1103/PhysRevE.74.026210 |
Abstract
We investigate the classical chaotic diffusion of atoms subjected to {\em pairs} of closely spaced pulses (`kicks) from standing waves of light (the $2\delta$-KP). Recent experimental studies with cold atoms implied an underlying classical diffusion of type very different from the well-known paradigm of Hamiltonian chaos, the Standard Map. The kicks in each pair are separated by a small time interval $\epsilon \ll 1$, which together with the kick strength $K$, characterizes the transport. Phase space for the $2\delta$-KP is partitioned into momentum `cells' partially separated by momentum-trapping regions where diffusion is slow. We present here an analytical derivation of the classical diffusion for a $2\delta$-KP including all important correlations which were used to analyze the experimental 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 find analytically, 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 $0.1\lesssim K\epsilon \lesssim 1$, where quantum localisation lengths $L \sim \hbar^{-0.75}$ are affected by fractal cell boundaries. We find an approximate asymptotic diffusion rate $D\propto K^3\epsilon$, in correspondence to a $D\propto K^3$ regime in the Standard Map associated with 'golden-ratio' cantori.
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"abstract": "We investigate the classical chaotic diffusion of atoms subjected to {\\em\npairs} of closely spaced pulses (`kicks) from standing waves of light (the\n$2\\delta$-KP). Recent experimental studies with cold atoms implied an\nunderlying classical diffusion of type very different from the well-known\nparadigm of Hamiltonian chaos, the Standard Map.\n The kicks in each pair are separated by a small time interval $\\epsilon \\ll\n1$, which together with the kick strength $K$, characterizes the transport.\nPhase space for the $2\\delta$-KP is partitioned into momentum `cells\u0027 partially\nseparated by momentum-trapping regions where diffusion is slow. We present here\nan analytical derivation of the classical diffusion for a $2\\delta$-KP\nincluding all important correlations which were used to analyze the\nexperimental data.\n We find a new asymptotic ($t \\to \\infty$) regime of `hindered\u0027 diffusion:\nwhile for the Standard Map the diffusion rate, for $K \\gg 1$, $D \\sim K^2/2[1-\nJ_2(K)..]$ oscillates about the uncorrelated, rate $D_0 =K^2/2$, we find\nanalytically, that the $2\\delta$-KP can equal, but never diffuses faster than,\na random walk rate.\n We argue this is due to the destruction of the important classical\n`accelerator modes\u0027 of the Standard Map.\n We analyze the experimental regime $0.1\\lesssim K\\epsilon \\lesssim 1$, where\nquantum localisation lengths $L \\sim \\hbar^{-0.75}$ are affected by fractal\ncell boundaries. We find an approximate asymptotic diffusion rate $D\\propto\nK^3\\epsilon$, in correspondence to a $D\\propto K^3$ regime in the Standard Map\nassociated with \u0027golden-ratio\u0027 cantori.",
"arxiv_id": "physics/0408088",
"authors": [
"M. M. A. Stocklin",
"T. S. Monteiro"
],
"categories": [
"physics.atom-ph"
],
"doi": "10.1103/PhysRevE.74.026210",
"title": "Classical diffusion in double-delta-kicked particles",
"url": "https://arxiv.org/abs/physics/0408088"
},
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