dorsal/arxiv
View SchemaFlow Equations for the Henon-Heiles Hamiltonian
| Authors | Daniel Cremers, Andreas Mielke |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9809086 |
| URL | https://arxiv.org/abs/quant-ph/9809086 |
| DOI | 10.1016/S0167-2789(98)00267-X |
Abstract
The Henon-Heiles Hamiltonian was introduced in 1964 as a mathematical model to describe the chaotic motion of stars in a galaxy. By canonically transforming the classical Hamiltonian to a Birkhoff-Gustavson normalform Delos and Swimm obtained a discrete quantum mechanical energy spectrum. The aim of the present work is to first quantize the classical Hamiltonian and to then diagonalize it using different variants of flow equations, a method of continuous unitary transformations introduced by Wegner in 1994. The results of the diagonalization via flow equations are comparable to those obtained by the classical transformation. In the case of commensurate frequencies the transformation turns out to be less lengthy. In addition, the dynamics of the quantum mechanical system are analyzed on the basis of the transformed observables.
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"abstract": "The Henon-Heiles Hamiltonian was introduced in 1964 as a mathematical model\nto describe the chaotic motion of stars in a galaxy. By canonically\ntransforming the classical Hamiltonian to a Birkhoff-Gustavson normalform Delos\nand Swimm obtained a discrete quantum mechanical energy spectrum. The aim of\nthe present work is to first quantize the classical Hamiltonian and to then\ndiagonalize it using different variants of flow equations, a method of\ncontinuous unitary transformations introduced by Wegner in 1994. The results of\nthe diagonalization via flow equations are comparable to those obtained by the\nclassical transformation. In the case of commensurate frequencies the\ntransformation turns out to be less lengthy. In addition, the dynamics of the\nquantum mechanical system are analyzed on the basis of the transformed\nobservables.",
"arxiv_id": "quant-ph/9809086",
"authors": [
"Daniel Cremers",
"Andreas Mielke"
],
"categories": [
"quant-ph",
"chao-dyn",
"nlin.CD"
],
"doi": "10.1016/S0167-2789(98)00267-X",
"title": "Flow Equations for the Henon-Heiles Hamiltonian",
"url": "https://arxiv.org/abs/quant-ph/9809086"
},
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