dorsal/arxiv
View SchemaQuantum eigenstates and (pseudo-)classical accelerator modes of the Delta-Kicked Accelerator
| Authors | Gabriel Lemarié, Keith Burnett |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0602204 |
| URL | https://arxiv.org/abs/quant-ph/0602204 |
Abstract
The quantum dynamics of a periodically driven system, the delta-kicked accelerator, is investigated in the semiclassical and pseudo-classical regimes, where quantum accelerator modes are observed. We construct the evolution operator of this classically chaotic system explicitly. If certain quantum resonance conditions are fullfilled, we show one can reduce the evolution operator to a finite matrix, whose eigenvectors are the quasi-eigenstates. These are represented by their Husimi functions. In so doing, we are able to directly compare the pure quantum states with the classical states. In the semiclassical regime, the quantum states are found to be related to the classical KAM tori and the classical accelerator modes. In contrast, the quasi-eigenstates do not lie on the $\epsilon$-classical trajectories in the pseudo-classical regime. This shows a clear and important distinction between semiclassicality and the new type of pseudo-classicality found by Fishman, Guarneri and Rebuzzini.
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"abstract": "The quantum dynamics of a periodically driven system, the delta-kicked\naccelerator, is investigated in the semiclassical and pseudo-classical regimes,\nwhere quantum accelerator modes are observed. We construct the evolution\noperator of this classically chaotic system explicitly. If certain quantum\nresonance conditions are fullfilled, we show one can reduce the evolution\noperator to a finite matrix, whose eigenvectors are the quasi-eigenstates.\nThese are represented by their Husimi functions. In so doing, we are able to\ndirectly compare the pure quantum states with the classical states. In the\nsemiclassical regime, the quantum states are found to be related to the\nclassical KAM tori and the classical accelerator modes. In contrast, the\nquasi-eigenstates do not lie on the $\\epsilon$-classical trajectories in the\npseudo-classical regime. This shows a clear and important distinction between\nsemiclassicality and the new type of pseudo-classicality found by Fishman,\nGuarneri and Rebuzzini.",
"arxiv_id": "quant-ph/0602204",
"authors": [
"Gabriel Lemari\u00e9",
"Keith Burnett"
],
"categories": [
"quant-ph"
],
"title": "Quantum eigenstates and (pseudo-)classical accelerator modes of the Delta-Kicked Accelerator",
"url": "https://arxiv.org/abs/quant-ph/0602204"
},
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