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Quantum dynamics of wave packets on phase space cells in nonlinearly coupled oscillators
Author(s) -
Brickmann Jürgen,
Schmidt Peter C.
Publication year - 1983
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.560230106
Subject(s) - phase space , harmonic oscillator , anharmonicity , physics , wave packet , space (punctuation) , wave function , quantum mechanics , phase transition , quantum , bar (unit) , philosophy , linguistics , meteorology
The time evolution of harmonic oscillator coherent states (minimum uncertainty wave packet) | Ψ μ located on regular and random von Neumann lattice points in phase space is analyzed for nonlinearly coupled anharmonic vibrational systems. The Henon–Heiles system is studied as an example. A quasiprobability measure \documentclass{article}\pagestyle{empty}\begin{document}$ \bar P_{\mu \mu '} $\end{document} is introduced to investigate the relative probabilities for the transition between phase space cells within a narrow energy range. The probability \documentclass{article}\pagestyle{empty}\begin{document}$ \bar P_{\mu \mu '} $\end{document} , as well as the information entropy S μ , is studied as a function of energy. A smooth transition from regular to chaotic motion is found indicated by a change of the fluctuations of these quantities as a function of energy.