Séminaire Optique/Spectro

Vendredi 31 Octobre 2014 à 11h00.

Far-infrared spectroscopy of NCNCS and its connection to quantum monodromy

''Imagine leaving your horse in a field, then walking in a circle around a nearby pumpkin, only to find upon returning to you initial position that your horse has turned into a cow! This is the flavour of monodromy, which describes how a mathematical entity (perhaps a function, or a geometrical shape, etc.) responds when a path is traced around a singularity. Monodromy plays a role in classical mechanics (for example, in the motion of a spherical pendulum) and in the quantum mechanics of a bending, rotating molecule. In this talk, we will discuss the implications of monodromy on far-infrared spectra of NCNCS from both at the Ohio State University, where pure rotational data were obtained, and at the Canadian Light Source, where rotation-vibration spectra were recorded. When a molecule that is bent when at equilibrium experiences both rotation and an excitation of its bending vibration, its motion is well-characterized by a potential that looks like the bottom of a champagne bottle: circularly symmetric, but with a ‘hump’ at its centre. In 1991, Larry Bates recognized that a classical particle moving under the influence of such a potential necessarily experienced effects imposed by monodromy (Bates, J. Applied Math. and Phys., vol. 42, pp. 837-847 (1991) ), and later Mark Child published a quantum version of the analysis (Child, J. Phys. A vol. 31, pp. 657-670 (1998) ). A prominent group of spectroscopists led by Manfred and Brenda Winnewisser and Frank de Lucia at the Ohio State University recognized about 10 years ago that NCNCS has properties suitable for illustrating the effects discussed by Child, since it has a low bending vibrational excitation (85 cm-1) of large amplitude, and since the ‘hump’ in the bending-rotation potential lies at ~300 cm-1, well below the next highest vibrational mode (~430 cm-1). The talk will describe the intensive experimental efforts required to generate the data required to create an experimental energy-momentum map for NCNCS that bears the fingerprints of monodromy. The semi-rigid bender procedure developed by Stephen Ross (PCCP vol. 12, pp. 8158-8189 (2010) ) is required to model the results. The effects observed in NCNCS will be compared to those in H2O and CH2, which are also influenced by monodromy.''