dorsal/arxiv
View SchemaApproximate integrals of motion and the quantum chaoticity problem
| Authors | V. E. Bunakov, I. B. Ivanov |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0101125 |
| URL | https://arxiv.org/abs/quant-ph/0101125 |
Abstract
The problem of existence and constructing of integrals of motion in stationary quantum mechanics and its connection with quantum chaoticity is discussed. It is shown that the earlier suggested quantum chaoticity criterion characterizes destruction of initial symmetry of regular system and of basis quantum numbers under influence of perturbation. The convergent procedure allowing to construct approximate integrals of motion in the form of non-trivial combinations depending on operators $(q,p)$ is suggested. Properties of the obtained integrals with complicated structure and the consequences of their existence for system's dynamics are discussed. The method is used for explicit construction and investigation of the approximate integrals in Henon-Heiles problem.
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"abstract": "The problem of existence and constructing of integrals of motion in\nstationary quantum mechanics and its connection with quantum chaoticity is\ndiscussed. It is shown that the earlier suggested quantum chaoticity criterion\ncharacterizes destruction of initial symmetry of regular system and of basis\nquantum numbers under influence of perturbation. The convergent procedure\nallowing to construct approximate integrals of motion in the form of\nnon-trivial combinations depending on operators $(q,p)$ is suggested.\nProperties of the obtained integrals with complicated structure and the\nconsequences of their existence for system\u0027s dynamics are discussed. The method\nis used for explicit construction and investigation of the approximate\nintegrals in Henon-Heiles problem.",
"arxiv_id": "quant-ph/0101125",
"authors": [
"V. E. Bunakov",
"I. B. Ivanov"
],
"categories": [
"quant-ph"
],
"title": "Approximate integrals of motion and the quantum chaoticity problem",
"url": "https://arxiv.org/abs/quant-ph/0101125"
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