On the Spectrum of Certain Non-Commutative Harmonic Oscillators and Semiclassical Analysis
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- Parmeggiani, A. Commun. Math. Phys. (2008) 279: 285. doi:10.1007/s00220-008-0436-2
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A localization and “cardinality” property, along with a multiplicity result, of the spectrum of certain 2 × 2 globally elliptic systems of ordinary differential operators, a class of vector-valued deformations of the classical harmonic oscillator called non-commutative harmonic oscillators, will be described here. The basic tool is the study of a semiclassical reference system.