Localization and delocalization of eigenmodes of harmonic oscillators
Localization and delocalization of eigenmodes of harmonic oscillators
We characterize quantum limits and semi-classical measures corresponding to sequences of eigenfunctions for systems of coupled quantum harmonic oscillators with arbitrary frequencies. The structure of the set of semi-classical measures turns out to depend strongly on the arithmetic relations between frequencies of each decoupled oscillator. In particular, we show that …