dorsal/arxiv
View SchemaClassical and quantum anomalous diffusion in a system of 2$\delta$-kicked Quantum Rotors
| Authors | Jiao Wang, Antonio M. Garcia-Garcia |
|---|---|
| Categories | |
| ArXiv ID | physics/0703105 |
| URL | https://arxiv.org/abs/physics/0703105 |
| DOI | 10.1142/S0217979208049480 |
| Journal | Int. J. Mod. Phys. B, 22, 5261 (2008) |
Abstract
We study the dynamics of cold atoms subjected to {\em pairs} of closely time-spaced $\delta$-kicks from standing waves of light. The classical phase space of this system is partitioned into momentum cells separated by trapping regions. In a certain range of parameters it is shown that the classical motion is well described by a process of anomalous diffusion. We investigate in detail the impact of the underlying classical anomalous diffusion on the quantum dynamics with special emphasis on the phenomenon of dynamical localization. Based on the study of the quantum density of probability, its second moment and the return probability we identify a region of weak dynamical localization where the quantum diffusion is still anomalous but the diffusion rate is slower than in the classical case. Moreover we examine how other relevant time scales such as the quantum-classical breaking time or the one related to the beginning of full dynamical localization are modified by the classical anomalous diffusion. Finally we discuss the relevance of our results for the understanding of the role of classical cantori in quantum mechanics.
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"abstract": "We study the dynamics of cold atoms subjected to {\\em pairs} of closely\ntime-spaced $\\delta$-kicks from standing waves of light. The classical phase\nspace of this system is partitioned into momentum cells separated by trapping\nregions. In a certain range of parameters it is shown that the classical motion\nis well described by a process of anomalous diffusion. We investigate in detail\nthe impact of the underlying classical anomalous diffusion on the quantum\ndynamics with special emphasis on the phenomenon of dynamical localization.\nBased on the study of the quantum density of probability, its second moment and\nthe return probability we identify a region of weak dynamical localization\nwhere the quantum diffusion is still anomalous but the diffusion rate is slower\nthan in the classical case. Moreover we examine how other relevant time scales\nsuch as the quantum-classical breaking time or the one related to the beginning\nof full dynamical localization are modified by the classical anomalous\ndiffusion. Finally we discuss the relevance of our results for the\nunderstanding of the role of classical cantori in quantum mechanics.",
"arxiv_id": "physics/0703105",
"authors": [
"Jiao Wang",
"Antonio M. Garcia-Garcia"
],
"categories": [
"physics.atom-ph",
"cond-mat.dis-nn",
"nlin.CD"
],
"doi": "10.1142/S0217979208049480",
"journal_ref": "Int. J. Mod. Phys. B, 22, 5261 (2008)",
"title": "Classical and quantum anomalous diffusion in a system of 2$\\delta$-kicked Quantum Rotors",
"url": "https://arxiv.org/abs/physics/0703105"
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