
Andreas Mielke
Institut for Theoretical Physics
RuprechtKarls University
Philosophenweg 19
D69120 Heidelberg
Germany
Tel.: ++49 6221 549431 (Secretary)
Fax: ++49 6221 549331
email:
mielke@tphys.uniheidelberg.de
Daniel Cremers, Andreas Mielke: Flow equations for the HénonHeiles Hamiltonian
Physica D126,
123135
(1999)
.
AbstractThe HénonHeiles Hamiltonian was introduced in 1964 [M. Hénon, C. Heiles: Astron. J. 69, 73 (1964)] as a mathematical model to describe the chaotic motion of stars in a galaxy. By canonically transforming the classical Hamiltonian to a BirkhoffGustavson 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 [Ann. Physik (Leipzig) 3, 77 (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.
BibTeXentry
@article{Cremers1999,
author="Daniel Cremers, Andreas Mielke",
title="Flow equations for the HénonHeiles Hamiltonian",
journal="Physica D",
volume="126",
pages="123135",
year="1999"
}
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Last changes: 5.7.2018.
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