Signed Phases and Fields Associated with Degeneracies

Details Signed Phases and Fields Associated with Degeneracies Signed Phases and Fields Associated with Degeneracies

2004-06-25

arxiv.org/abs/quant-ph/0406194v1

Acta Phys. et Chim., 34-35, 283 (2002)

Physics

Quantum Physics

34 pages, 1 figure

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Signed Phases and Fields Associated with Degeneracies does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Signed Phases and Fields Associated with Degeneracies, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Signed Phases and Fields Associated with Degeneracies will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-206781