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.
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
Măntoiu, Marius 1
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TY - JOUR AU - Măntoiu, Marius TI - Rieffel’s pseudodifferential calculus and spectral analysis of quantum Hamiltonians JO - Annales de l'Institut Fourier PY - 2012 SP - 1551 EP - 1580 VL - 62 IS - 4 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.2729/ DO - 10.5802/aif.2729 LA - en ID - AIF_2012__62_4_1551_0 ER -
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Măntoiu, Marius. Rieffel’s pseudodifferential calculus and spectral analysis of quantum Hamiltonians. Annales de l'Institut Fourier, Volume 62 (2012) no. 4, pp. 1551-1580. doi : 10.5802/aif.2729. https://aif.centre-mersenne.org/articles/10.5802/aif.2729/
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