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1983
2.	Ramaswamy, Ramakrishna Chaotic motions in vibrating molecules: The generalized Henon-Heiles model Journal Article Chemical Physics, 76 (1), pp. 15–24, 1983, ISSN: 03010104. Abstract \| Links \| BibTeX \| Tags: Chaos, Henon-Heiles @article{Ramaswamy1983, title = {Chaotic motions in vibrating molecules: The generalized Henon-Heiles model}, author = {Ramakrishna Ramaswamy}, url = {https://ramramaswamy.org/papers/018.pdf}, doi = {10.1016/0301-0104(83)85046-0}, issn = {03010104}, year = {1983}, date = {1983-01-01}, journal = {Chemical Physics}, volume = {76}, number = {1}, pages = {15–24}, abstract = {The method of avoided crossings is applied to a simple molecular model, the generalized Henon-Heiles system of coupled oscillators. The aim here is to determine the onset of wide-spread chaotic motions. The method is used to locate, in a simple manner, the resonances that lead to chaotic motions for different choices of parameters, wherein the frequencies of the unperturbed oscillators are in the ratio 3 : 4 and 7 : 13. The accuracy of the prediction is verified against numerical calculations of classical trajectories. textcopyright 1983.}, keywords = {Chaos, Henon-Heiles}, pubstate = {published}, tppubtype = {article} } Close The method of avoided crossings is applied to a simple molecular model, the generalized Henon-Heiles system of coupled oscillators. The aim here is to determine the onset of wide-spread chaotic motions. The method is used to locate, in a simple manner, the resonances that lead to chaotic motions for different choices of parameters, wherein the frequencies of the unperturbed oscillators are in the ratio 3 : 4 and 7 : 13. The accuracy of the prediction is verified against numerical calculations of classical trajectories. textcopyright 1983. Close https://ramramaswamy.org/papers/018.pdf doi:10.1016/0301-0104(83)85046-0 Close
1981
1.	Ramaswamy, R; Marcus, R A Perturbative examination of avoided crossings Journal Article The Journal of Chemical Physics, 74 (2), pp. 1379–1384, 1981, ISSN: 0021-9606. Abstract \| Links \| BibTeX \| Tags: Henon-Heiles, Nonintegrable Hamiltonian Systems, Perturbation @article{Ramaswamy1981, title = {Perturbative examination of avoided crossings}, author = {R Ramaswamy and R A Marcus}, url = {https://doi.org/10.1063/1.441201}, doi = {10.1063/1.441201}, issn = {0021-9606}, year = {1981}, date = {1981-01-15}, journal = {The Journal of Chemical Physics}, volume = {74}, number = {2}, pages = {1379–1384}, abstract = {Quantum perturbation theory is used to examine the eigenvalues of a nonseparable Hamiltonian system in the classically regular and irregular regimes. As a function of the perturbation parameter, the eigenvalues obtained by exact (matrix diagonalization) methods undergo an avoided crossing. In the present paper perturbation theory is used as an approximate method to predict the locations of such avoided crossings in energy‐parameter space. The sparsity of such avoided crossings in the Hénon–Heiles system is seen to produce regular sequences in the eigenvalues even when the classical motion is predominantly chaotic.}, keywords = {Henon-Heiles, Nonintegrable Hamiltonian Systems, Perturbation}, pubstate = {published}, tppubtype = {article} } Close Quantum perturbation theory is used to examine the eigenvalues of a nonseparable Hamiltonian system in the classically regular and irregular regimes. As a function of the perturbation parameter, the eigenvalues obtained by exact (matrix diagonalization) methods undergo an avoided crossing. In the present paper perturbation theory is used as an approximate method to predict the locations of such avoided crossings in energy‐parameter space. The sparsity of such avoided crossings in the Hénon–Heiles system is seen to produce regular sequences in the eigenvalues even when the classical motion is predominantly chaotic. Close https://doi.org/10.1063/1.441201 doi:10.1063/1.441201 Close

1983

1981