We show here that the spectrum of the family of non-commutative harmonic oscillators Q_(α,β)(x, D) for α, β ∈ R+ in the range αβ = 1 is [0, + ∞) and is entirely essential spectrum. The previous existing results concern the case αβ > 1 (case in which Q_(α,β)(x, D) is globally elliptic with a discrete spectrum whose qualitative properties are being extensively studied), and ours therefore extend the picture to the range of parameters αβ ≥ 1.
On the essential spectrum of certain non-commutative oscillators / Alberto Parmeggiani; Alberto Venni. - In: JOURNAL OF MATHEMATICAL PHYSICS. - ISSN 0022-2488. - STAMPA. - 54:12(2013), pp. 121507-1-121507-10. [10.1063/1.4850876]
On the essential spectrum of certain non-commutative oscillators
PARMEGGIANI, ALBERTO;VENNI, ALBERTO
2013
Abstract
We show here that the spectrum of the family of non-commutative harmonic oscillators Q_(α,β)(x, D) for α, β ∈ R+ in the range αβ = 1 is [0, + ∞) and is entirely essential spectrum. The previous existing results concern the case αβ > 1 (case in which Q_(α,β)(x, D) is globally elliptic with a discrete spectrum whose qualitative properties are being extensively studied), and ours therefore extend the picture to the range of parameters αβ ≥ 1.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
