Classical diffusion in double-delta-kicked particles

• Published in: arXiv.org
• Main Authors: Stocklin, M M A, Monteiro, T S
• Format: Paper
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 12.04.2006
• Subjects: Asymptotic properties; Cold atoms; Correlation analysis; Diffusion rate; Momentum; Random walk; Standing waves
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.0408088

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.