Geodesic
Rieffel’s pseudodifferential calculus and spectral analysis of quantum Hamiltonians
[Calcul pseudodifferentiel de Rieffel et analyse spectrale des Hamiltoniens quantiques]
Măntoiu, Marius1 
1 Universidad de Chile, Facultad de Ciencias, Departamento de Matemáticas, Las Palmeras 3425, Casilla 653 Santiago, Chile
Annales de l'Institut Fourier, Tome 62 (2012) no. 4, pp. 1551-1580.

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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.

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.

DOI : 10.5802/aif.2729
Classification : 35S05, 81Q10, 46L55, 47C15
Keywords: Pseudodifferential operator, essential spectrum, random operator, semiclassical limit, noncommutative dynamical system
Mots-clés : Opérateur pseudodifferentiel, spectre essentiel, opérateur aléatoire, limite semiclassique, systéme dynamique non-commutative

Măntoiu, Marius 1

1 Universidad de Chile, Facultad de Ciencias, Departamento de Matemáticas, Las Palmeras 3425, Casilla 653 Santiago, Chile 
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Măntoiu, Marius. Rieffel’s pseudodifferential calculus and spectral analysis of quantum Hamiltonians. Annales de l'Institut Fourier, Tome 62 (2012) no. 4, pp. 1551-1580. doi : 10.5802/aif.2729. http://geodesic.mathdoc.fr/articles/10.5802/aif.2729/

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