Rieffel’s pseudodifferential calculus and spectral analysis of quantum Hamiltonians

Marius Măntoiu[1]

  • [1] Universidad de Chile, Facultad de Ciencias, Departamento de Matemáticas, Las Palmeras 3425, Casilla 653 Santiago, Chile

Annales de l’institut Fourier (2012)

  • Volume: 62, Issue: 4, page 1551-1580
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Măntoiu, Marius. "Rieffel’s pseudodifferential calculus and spectral analysis of quantum Hamiltonians." Annales de l’institut Fourier 62.4 (2012): 1551-1580. <http://eudml.org/doc/251133>.

@article{Măntoiu2012,
abstract = {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.},
affiliation = {Universidad de Chile, Facultad de Ciencias, Departamento de Matemáticas, Las Palmeras 3425, Casilla 653 Santiago, Chile},
author = {Măntoiu, Marius},
journal = {Annales de l’institut Fourier},
keywords = {Pseudodifferential operator; essential spectrum; random operator; semiclassical limit; noncommutative dynamical system; pseudodifferential operator},
language = {eng},
number = {4},
pages = {1551-1580},
publisher = {Association des Annales de l’institut Fourier},
title = {Rieffel’s pseudodifferential calculus and spectral analysis of quantum Hamiltonians},
url = {http://eudml.org/doc/251133},
volume = {62},
year = {2012},
}

TY - JOUR
AU - Măntoiu, Marius
TI - Rieffel’s pseudodifferential calculus and spectral analysis of quantum Hamiltonians
JO - Annales de l’institut Fourier
PY - 2012
PB - Association des Annales de l’institut Fourier
VL - 62
IS - 4
SP - 1551
EP - 1580
AB - 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.
LA - eng
KW - Pseudodifferential operator; essential spectrum; random operator; semiclassical limit; noncommutative dynamical system; pseudodifferential operator
UR - http://eudml.org/doc/251133
ER -

References

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