Rieffel’s pseudodifferential calculus and spectral analysis of quantum Hamiltonians
[Calcul pseudodifferentiel de Rieffel et analyse spectrale des Hamiltoniens quantiques]
Măntoiu, Marius
Annales de l'Institut Fourier, Tome 62 (2012), p. 1551-1580 / Harvested from Numdam
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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.

Publié le : 2012-01-01
DOI : https://doi.org/10.5802/aif.2729
Classification:  35S05,  81Q10,  46L55,  47C15
Mots clés: Opérateur pseudodifferentiel, spectre essentiel, opérateur aléatoire, limite semiclassique, systéme dynamique non-commutative 
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     title = {Rieffel's pseudodifferential calculus and spectral analysis of quantum Hamiltonians},
     journal = {Annales de l'Institut Fourier},
     volume = {62},
     year = {2012},
     pages = {1551-1580},
     doi = {10.5802/aif.2729},
     zbl = {1253.35232},
     mrnumber = {3025750},
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     url = {http://dml.mathdoc.fr/item/AIF_2012__62_4_1551_0}
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Măntoiu, Marius. Rieffel’s pseudodifferential calculus and spectral analysis of quantum Hamiltonians. Annales de l'Institut Fourier, Tome 62 (2012) pp. 1551-1580. doi : 10.5802/aif.2729. http://gdmltest.u-ga.fr/item/AIF_2012__62_4_1551_0/

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