Rieffel’s pseudodifferential calculus and spectral analysis of quantum Hamiltonians  [ Calcul pseudodifferentiel de Rieffel et analyse spectrale des Hamiltoniens quantiques ]
Annales de l'Institut Fourier, Tome 62 (2012) no. 4, p. 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.
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
@article{AIF_2012__62_4_1551_0,
     author = {M\u antoiu, Marius},
     title = {Rieffel's pseudodifferential calculus and spectral analysis of quantum Hamiltonians},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {62},
     number = {4},
     year = {2012},
     pages = {1551-1580},
     doi = {10.5802/aif.2729},
     mrnumber = {3025750},
     zbl = {1253.35232},
     language = {en},
     url = {http://www.numdam.org/item/AIF_2012__62_4_1551_0}
}
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://www.numdam.org/item/AIF_2012__62_4_1551_0/

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