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Symmetry and the Entangled Ro-Vibrational Quantum States of a Fluxional Molecule

Banff International Research Station for Mathematical Innovation and Discovery

Separation of rotational and vibrational motion is a key concept in the analysis of the dynamics of isolated molecules. Approximate separability does not only hold for rigid or semi-rigid molecules but often works quite well even in the presence of large amplitude motion. While the precise analysis of spectroscopic experiments often requires to account for rotation-vibration couplings, a separable ansatz typically provides a valid zero order description on which further refinements can be based. A fundamentally different situation is encountered if fluxional molecules like $AB_n$ or $B_n$ with n>4 are considered. Then fundamental symmetry arguments require the complete breakdown of the separability of rotational and internal motion. Rotational and internal motion must always be entangled. The talk will discuss fundamental issues related with the separation of rotational and vibrational motion in fluxional molecules. Challenges regarding the application of group and representation theory to the problem will be highlighted. In addition, numerical results for a prototypical example, the $CH^+_5$ molecular cation, will be shown.

Mathematics; Quantum theory; Partial differential equations; Applied computer science

video/mp4

Author affiliation: Bielefeld University

2016-07-29

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/58585

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/