no. 6
Partial Differential Equations
Results dealing with the behavior of the integrated density of states of random divergence operators
[Des résultats sur le comportement de la densité d'états integrèe de l'opérateur de divergence aléatoire]

Présenté par : Gilles Lebeau

Najar, Hatem1
1 I.P.E.I. Monastir, rue Ibn Eljazzar, 5019 Monastir, Tunisia
Comptes Rendus. Mathématique, Tome 344 (2007) no. 6, pp. 367-372.

Dans cette Note on généralise et en améliore des résultats prouvés pour les opérateurs acoustique par Najar (2003). Il concerne le comportement de la densité d'états intégrée de l'opérateur de divergence aléatoire ayant la forme Hω=∑i,j=1d∂xiai,j(ω,x)∂xj aux bords internes du spectre.

In this Note we generalize and improve results proven for acoustic operators given by Najar in 2003. It deals with the behavior of the integrated density of states of random divergence operators of the form Hω=∑i,j=1d∂xiai,j(ω,x)∂xj on the internal band edges of the spectrum.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2007.02.001
Najar, Hatem 1

1 I.P.E.I. Monastir, rue Ibn Eljazzar, 5019 Monastir, Tunisia 
@article{CRMATH_2007__344_6_367_0,
     author = {Najar, Hatem},
     title = {Results dealing with the behavior of the integrated density of states of random divergence operators},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {367--372},
     publisher = {Elsevier},
     volume = {344},
     number = {6},
     year = {2007},
     doi = {10.1016/j.crma.2007.02.001},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.crma.2007.02.001/}
}
TY  - JOUR
AU  - Najar, Hatem
TI  - Results dealing with the behavior of the integrated density of states of random divergence operators
JO  - Comptes Rendus. Mathématique
PY  - 2007
SP  - 367
EP  - 372
VL  - 344
IS  - 6
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.crma.2007.02.001/
DO  - 10.1016/j.crma.2007.02.001
LA  - en
ID  - CRMATH_2007__344_6_367_0
ER  - 
%0 Journal Article
%A Najar, Hatem
%T Results dealing with the behavior of the integrated density of states of random divergence operators
%J Comptes Rendus. Mathématique
%D 2007
%P 367-372
%V 344
%N 6
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.crma.2007.02.001/
%R 10.1016/j.crma.2007.02.001
%G en
%F CRMATH_2007__344_6_367_0
Najar, Hatem. Results dealing with the behavior of the integrated density of states of random divergence operators. Comptes Rendus. Mathématique, Tome 344 (2007) no. 6, pp. 367-372. doi : 10.1016/j.crma.2007.02.001. http://www.numdam.org/articles/10.1016/j.crma.2007.02.001/

[1] Dembo, A.; Zeitouni, O. Large Deviation and Applications, Jones and Bartlett Publishers, Boston, MA, 1992

[2] Figotin, A.; Klein, A. Localization of classical waves I: Acoustic waves, Comm. Math. Phys., Volume 180 (1996), pp. 439-482

[3] Figotin, A.; Kuchment, P. Band-gap structure of spectra of periodic dielectric and acoustic media. II. Two-dimensional photonic crystals, SIAM J. Math., Volume 56 (1996) no. 6, pp. 1561-1620

[4] R. Hempel, O. Post, Spectral gaps for periodic elliptic operators with high contrast: an overview, in: Progress in Analysis, vols. I, II, Berlin, 2001, 2003, pp. 577–587

[5] Kirsch, W.; Martinelli, F. On the spectrum of Schrödinger operators with a random potential, Comm. Math. Phys., Volume 85 (1982), pp. 329-350

[6] Kirsch, W. Random Schrödinger operators, Lecture Notes in Phys., vol. 345, Springer-Verlag, Berlin, 1989, pp. 264-370

[7] Klopp, F. Internal Lifshitz tails for random perturbations of periodic Schrödinger operators, Duke Math. J., Volume 98 (1999) no. 2, pp. 335-396

[8] Klopp, F. Une remarque à propos des asymptotiques de Lifshitz internes, C. R. Math. Acad. Sci. Paris, Ser. I, Volume 335 (2002) no. 1, pp. 87-92

[9] Najar, H. Lifshitz tails for random acoustic operators, J. Math. Phys., Volume 44 (2003) no. 4, pp. 1842-1867

[10] Najar, H. Asymptotic behavior of the integrated density of states of acoustic operator with long range random perturbations, J. Stat. Phys., Volume 115 (2003) no. 4, pp. 955-977

[11] Pastur, L.; Figotin, A. Spectra of Random and Almost-Periodic Operators, Springer-Verlag, Berlin, 1992

[12] Reed, M.; Simon, B. Methods of Modern Mathematical, vol. IV: Analysis of Operators, Academic Press, New York, 1978

[13] Simon, B. Lifshitz tails for the Anderson models, J. Stat. Phys., Volume 38 (1985), pp. 65-76

[14] Stollmann, P. Caught by Disorder Bounded States in Random Media, Birkhäuser, Boston, 2001

Cité par Sources :