dorsal/arxiv
View SchemaUnderstanding highly excited states via parametric variations
| Authors | A. Semparithi, V. Charulatha, S. Keshavamurthy |
|---|---|
| Categories | |
| ArXiv ID | physics/0205068 |
| URL | https://arxiv.org/abs/physics/0205068 |
| DOI | 10.1063/1.1527922 |
Abstract
Highly excited vibrational states of an isolated molecule encode the vibrational energy flow pathways in the molecule. Recent studies have had spectacular success in understanding the nature of the excited states mainly due to the extensive studies of the classical phase space structures and their bifurcations. Such detailed classical-quantum correspondence studies are presently limited to two or quasi two dimensional systems. One of the main reasons for such a constraint has to do with the problem of visualization of relevant objects like surface of sections and Wigner or Husimi distributions associated with an eigenstate. This neccesiates various alternative techniques which are more algebraic than geometric in nature. In this work we introduce one such method based on parametric variation of the eigenvalues of a Hamiltonian. It is shown that the level velocities are correlated with the phase space nature of the corresponding eigenstates. A semiclassical expression for the level velocities of a single resonance Hamiltonian is derived which provides theoretical support for the correlation. We use the level velocities to dynamically assign the highly excited states of a model spectroscopic Hamiltonian in the mixed phase space regime. The effect of bifurcations on the level velocities is briefly discussed using a recently proposed spectroscopic Hamiltonian for the HCP molecule.
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"abstract": "Highly excited vibrational states of an isolated molecule encode the\nvibrational energy flow pathways in the molecule. Recent studies have had\nspectacular success in understanding the nature of the excited states mainly\ndue to the extensive studies of the classical phase space structures and their\nbifurcations. Such detailed classical-quantum correspondence studies are\npresently limited to two or quasi two dimensional systems. One of the main\nreasons for such a constraint has to do with the problem of visualization of\nrelevant objects like surface of sections and Wigner or Husimi distributions\nassociated with an eigenstate. This neccesiates various alternative techniques\nwhich are more algebraic than geometric in nature. In this work we introduce\none such method based on parametric variation of the eigenvalues of a\nHamiltonian. It is shown that the level velocities are correlated with the\nphase space nature of the corresponding eigenstates. A semiclassical expression\nfor the level velocities of a single resonance Hamiltonian is derived which\nprovides theoretical support for the correlation. We use the level velocities\nto dynamically assign the highly excited states of a model spectroscopic\nHamiltonian in the mixed phase space regime. The effect of bifurcations on the\nlevel velocities is briefly discussed using a recently proposed spectroscopic\nHamiltonian for the HCP molecule.",
"arxiv_id": "physics/0205068",
"authors": [
"A. Semparithi",
"V. Charulatha",
"S. Keshavamurthy"
],
"categories": [
"physics.chem-ph",
"nlin.CD"
],
"doi": "10.1063/1.1527922",
"title": "Understanding highly excited states via parametric variations",
"url": "https://arxiv.org/abs/physics/0205068"
},
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