Rieffel’s pseudodifferential calculus and spectral analysis of quantum Hamiltonians

Măntoiu, Marius

Annales de l'Institut Fourier, Tome 62 (2012) no. 4, pp. 1551-1580.

On utilise les propriétés functorielles du calcul pseudodifferentiel de Rieffel pour étudier des familles d’opérateurs associés à des systèmes dynamiques topologiques sur lesquelles agit un espace symplectique. On obtient des informations sur le spectre et le spectre essentiel à partir de la structure des quasi-orbites du système dynamique. Le comportement semi-classique des familles des spectres est aussi étudié.

We use the functorial properties of Rieffel’s pseudodifferential calculus to study families of operators associated to topological dynamical systems acted by a symplectic space. Information about the spectra and the essential spectra are extracted from the quasi-orbit structure of the dynamical system. The semi-classical behavior of the families of spectra is also studied.

Classification : 35S05, 81Q10, 46L55, 47C15
Keywords: Pseudodifferential operator, essential spectrum, random operator, semiclassical limit, noncommutative dynamical system
Mot clés : Opérateur pseudodifferentiel, spectre essentiel, opérateur aléatoire, limite semiclassique, systéme dynamique non-commutative

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