dorsal/arxiv
View SchemaSigned Phases and Fields Associated with Degeneracies
| Authors | R. Englman, A. Yahalom |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0406194 |
| URL | https://arxiv.org/abs/quant-ph/0406194 |
| Journal | Acta Phys. et Chim., 34-35, 283 (2002) |
Abstract
In the first part, expressions are given for the {\it sign} of the topological angle that is acquired upon making a loop around a degeneracy ("conical intersection") point of two molecular energy surfaces. The expressions involve the partial derivatives (with respect to the nuclear coordinates) of the matrix elements of the coupling Hamiltonian. Examples are given of a few studied cases, such as of excited states that have topological angles with a sign opposite to those in the ground states. In the second part, the two dimensional (or two parameter) situation that characterizes a conical intersection (ci) between potential surfaces in a polyatomic molecule is constructed as a limiting case of the three dimensional Dirac-monopole situation. For an electron occupying a twofold state, we obtain both the "magnetic-field" (or curl-field) and the tensorial (or Yang-Mills-) field (which is the sum of a curl and of a vector- product term). These pseudo- fields represent the reaction of the electron on the nuclear motion via the nonadiabatic coupling terms (NACTs). We find that both fields are aligned with the orthogonal, (so called) seam directions of the ci and are zero everywhere outside the seam, but they differ as regards the flux that they produce. In a two-state situation, the fields are representation dependent and the values of, e.g., the fluxes depend on the state that the electron occupies. The angular dependence of the NACTs and the fields calculated from a general linearly coupled model agrees with recently computed results for $C_2 H$ [A.M. Mebel, M. Baer and S.H. Lin, J.Chem. Phys. {\bf 115} 3673 (2001)]. An effective-Hamiltonian formalism is proposed for experimentally observing and distinguishing between the different fields.
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"abstract": "In the first part, expressions are given for the {\\it sign} of the\ntopological angle that is acquired upon making a loop around a degeneracy\n(\"conical intersection\") point of two molecular energy surfaces. The\nexpressions involve the partial derivatives (with respect to the nuclear\ncoordinates) of the matrix elements of the coupling Hamiltonian. Examples are\ngiven of a few studied cases, such as of excited states that have topological\nangles with a sign opposite to those in the ground states. In the second part,\nthe two dimensional (or two parameter) situation that characterizes a conical\nintersection (ci) between potential surfaces in a polyatomic molecule is\nconstructed as a limiting case of the three dimensional Dirac-monopole\nsituation. For an electron occupying a twofold state, we obtain both the\n\"magnetic-field\" (or curl-field) and the tensorial (or Yang-Mills-) field\n(which is the sum of a curl and of a vector- product term). These pseudo-\nfields represent the reaction of the electron on the nuclear motion via the\nnonadiabatic coupling terms (NACTs). We find that both fields are aligned with\nthe orthogonal, (so called) seam directions of the ci and are zero everywhere\noutside the seam, but they differ as regards the flux that they produce. In a\ntwo-state situation, the fields are representation dependent and the values of,\ne.g., the fluxes depend on the state that the electron occupies. The angular\ndependence of the NACTs and the fields calculated from a general linearly\ncoupled model agrees with recently computed results for $C_2 H$ [A.M. Mebel, M.\nBaer and S.H. Lin, J.Chem. Phys. {\\bf 115} 3673 (2001)]. An\neffective-Hamiltonian formalism is proposed for experimentally observing and\ndistinguishing between the different fields.",
"arxiv_id": "quant-ph/0406194",
"authors": [
"R. Englman",
"A. Yahalom"
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"journal_ref": "Acta Phys. et Chim., 34-35, 283 (2002)",
"title": "Signed Phases and Fields Associated with Degeneracies",
"url": "https://arxiv.org/abs/quant-ph/0406194"
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