Topologically coupled energy bands in molecules

Frederic Faure (1) , Boris I Zhilinskií (2)

1 IF - Institut Fourier
2 LPCA - Laboratoire de Physico-Chimie de l'Atmosphère

We propose a concrete application of the Atiyah-Singer index formula in molecular physics, giving the exact number of levels in energy bands, in terms of vector bundles topology. The formation of topologically coupled bands is demonstrated. This phenomenon is expected to be present in many quantum systems.

Mots clés: : Born-Oppenheimer approximation; Mole ular spe tra; Ve tor bundles; Index formula; Semi- lassi al analysis; : Born-Oppenheimer approximation

Domaines: Physique Quantique [quant-ph]

Frederic Faure, Boris I Zhilinskií. Topologically coupled energy bands in molecules. Physics Letters A, 2002, 302, pp.242-252. ⟨hal-00383056⟩