On a class of anisotropic asymptotically periodic Hamiltonians

Olivier Rodot

doi:10.1016/S1631-073X(02)02301-4

On a class of anisotropic asymptotically periodic Hamiltonians
[Hamiltoniens anisotropes asymptotiquement périodiques]

Olivier Rodot ¹

¹ Département de mathématiques, Université de Cergy-Pontoise, 2, avenue Adolphe Chauvin, 95302 Cergy-Pontoise cedex, France

Comptes Rendus. Mathématique, Volume 334 (2002) no. 7, pp. 575-579.

Résumé
Abstract

Nous construisons une $C^{*}$ -algèbre $ℭ$ adaptée au traitement des systèmes quantiques anisotropes asymptotiquement périodiques et nous calculons son quotient par l'algèbre des opérateurs compacts. Nous décrivons alors les opérateurs auto-adjoints affiliés à $ℭ$ et leurs spectres essentiels.

We construct a $C^{*}$ -algebra $ℭ$ proper to an anisotropic asymptotically periodic quantum system and we compute its quotient by the algebra of compact operators. We describe then the self-adjoint operators affiliated to $ℭ$ and their essential spectrum.

Reçu le : 2002-01-25
Accepté le : 2002-02-04
Publié le : 2002-01-01

DOI : 10.1016/S1631-073X(02)02301-4

Affiliations des auteurs :

Olivier Rodot ¹

¹ Département de mathématiques, Université de Cergy-Pontoise, 2, avenue Adolphe Chauvin, 95302 Cergy-Pontoise cedex, France

@article{CRMATH_2002__334_7_575_0,
     author = {Olivier Rodot},
     title = {On a class of anisotropic asymptotically periodic {Hamiltonians}},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {575--579},
     publisher = {Elsevier},
     volume = {334},
     number = {7},
     year = {2002},
     doi = {10.1016/S1631-073X(02)02301-4},
     language = {en},
}

TY  - JOUR
AU  - Olivier Rodot
TI  - On a class of anisotropic asymptotically periodic Hamiltonians
JO  - Comptes Rendus. Mathématique
PY  - 2002
SP  - 575
EP  - 579
VL  - 334
IS  - 7
PB  - Elsevier
DO  - 10.1016/S1631-073X(02)02301-4
LA  - en
ID  - CRMATH_2002__334_7_575_0
ER  -

%0 Journal Article
%A Olivier Rodot
%T On a class of anisotropic asymptotically periodic Hamiltonians
%J Comptes Rendus. Mathématique
%D 2002
%P 575-579
%V 334
%N 7
%I Elsevier
%R 10.1016/S1631-073X(02)02301-4
%G en
%F CRMATH_2002__334_7_575_0

Olivier Rodot. On a class of anisotropic asymptotically periodic Hamiltonians. Comptes Rendus. Mathématique, Volume 334 (2002) no. 7, pp. 575-579. doi : 10.1016/S1631-073X(02)02301-4. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)02301-4/

Bibliographie
Cité par

[1] F. Bloch Über die Quantenmechanik der Elektronen in Kristallgittern, Z. Phys., Volume 52 (1928), pp. 555-600

[2] M. Damak, V. Georgescu, $C^{*}$ -algebras related to the N-body problem and the self-adjoint operators affiliated to them, available as preprint 99-482 at http://www.ma.utexas.edu/mp_arc/

[3] E.B. Davies; B. Simon Scattering theory for systems with different spatial asymptotics on the left and right, Comm. Math. Phys., Volume 63 (1978), pp. 277-301

[4] I.M. Gel'fand Expansion in eigenfunctions of an equation with periodic coefficients, Dokl. Akad. Nauk SSSR, Volume 73 (1950), pp. 1117-1120 (in Russian)

[5] V. Georgescu, A. Iftimovici, $C^{*}$ -algebras and spectral analysis of quantum systems, in: Proceedings of the OAMP Conference, Constanta, 2001, to appear

[6] V. Georgescu, A. Iftimovici, $C^{*}$ -algebras of energy observables, Preprint 9/2001, Université de Cergy-Pontoise, pp. 1–120, also available at http://www.ma.utexas.edu/mp_arc

[7] T.M. Roberts Scattering for step-periodic potentials in one dimension, J. Math. Phys., Volume 31 (1990) no. 9, pp. 2181-2191

[8] E.C. Titchmarsh Eigenfunction Expansions Associated with Second Order Differential Equations, Clarendon Press, Oxford, 1962

Cité par Sources :

Commentaires - Politique