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Sub-exponential decay of operator kernels for functions of generalized Schrödinger operators
Author(s):
Jean-Marc
Bouclet;
François
Germinet;
Abel
Klein
Journal:
Proc. Amer. Math. Soc.
132
(2004),
2703-2712.
MSC (2000):
Primary 81Q10, 47F05;
Secondary 35P05
Posted:
April 21, 2004
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Abstract:
We study the decay at large distances of operator kernels of functions of generalized Schrödinger operators. We prove sub-exponential decay for functions in Gevrey classes and exponential decay for real analytic functions.
References:
-
- [CKM]
- R. Carmona, A. Klein, and F. Martinelli: Anderson localization for Bernoulli and other singular potentials, Commun. Math. Phys. 108, 41-66 (1987). MR 88f:82027
- [CoTh]
- J. M. Combes and L. Thomas: Asymptotic behavior of eigenfunctions for multi-particle Schrödinger operators, Commun. Math. Phys. 34, 251-270 (1973). MR 52:12611
- [DSS]
- D. Damanik, R. Sims, and G. Stolz: Localization for one-dimensional, continuum, Bernoulli-Anderson models, Duke Math. J. 114, 59-100 (2002). MR 2003h:82048
- [Da1]
- E. B. Davies: Kernel estimates for functions of second order elliptic operators, Quart. J. Math. Oxford Ser. (2) 39, 37-46 (1988). MR 89c:35123
- [Da2]
- E. B. Davies: Heat kernels and spectral theory, Cambridge University Press, Cambridge, 1990. MR 92a:35035
- [DBG]
- S. De Bièvre and F. Germinet: Dynamical localization for the random dimer Schrödinger operator, J. Statist. Phys. 98, 1135-1147 (2000). MR 2000m:82053
- [DiSj]
- M. Dimassi and J. Sjöstrand: Spectral asymptotics in the semi-classical limit, London Math. Soc. Lecture Note Series 268, Cambridge University Press, Cambridge, 1999. MR 2001b:35237
- [ElGr]
- P. Elbau and G. M. Graf: Equality of bulk and edge Hall conductance revisited, Commun. Math. Phys. 229, 415-432 (2002). MR 2003h:81264
- [GKT]
- F. Germinet, A. Kiselev, and S. Tcheremchantsev: Transfer matrices and transport for 1D Schrödinger operators with singular spectrum, Ann. Inst. Fourier, to appear.
- [GK1]
- F. Germinet and A. Klein: Bootstrap multiscale analysis and localization in random media, Commun. Math. Phys. 222, 415-448 (2001). MR 2002m:82035
- [GK2]
- F. Germinet and A. Klein: Operator kernel estimates for functions of generalized Schrödinger operators, Proc. Amer. Math. Soc. 131, 911-920 (2003). MR 2003k:47067
- [GK3]
- F. Germinet and A. Klein: A characterization of the metal-insulator transport transition, submitted.
- [GK4]
- F. Germinet and A. Klein: The Anderson metal-insulator transport transition, to appear in Contemp. Math.
- [HeSj]
- B. Helffer and S. Sjöstrand: Équation de Schrödinger avec champ magnétique et équation de Harper, in Schrödinger operators, H. Holden and A. Jensen, eds., Lecture Notes in Physics, vol. 345, Springer-Verlag, Berlin, 1989, pp. 118-197. MR 91g:35078
- [Ho]
- L. Hörmander: The analysis of linear partial differential operators. I. Distribution theory and Fourier analysis, Second edition. Springer Study Edition, Springer-Verlag, Berlin, 1990. MR 91m:35001b
- [JSBS]
- S. Jitomirskaya, H. Schulz-Baldes, and G. Stolz: Delocalization in random polymer models, Commun. Math. Phys. 233, 27-48 (2003).
- [KLS]
- A. Klein, J. Lacroix, and A. Speis: Localization for the Anderson model on a strip with singular potentials, J. Funct. Anal. 94, 135-155 (1990). MR 92c:82060
- [Si]
- B. Simon: Schrödinger semi-groups, Bull. Amer. Math. Soc. (N.S.) 7, 447-526 (1982). MR 86b:81001a
- [Tc]
- S. Tcheremchantsev: Dynamical analysis of Schrödinger operators with sparse potential, Comm. Math. Phys., to appear.
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Additional Information:
Jean-Marc
Bouclet
Affiliation:
UMR 8524 CNRS, UFR de Mathématiques, Université de Lille 1, F-59655 Villeneuve d'Ascq Cédex, France
Email:
Jean-Marc.Bouclet@agat.univ-lille1.fr
François
Germinet
Affiliation:
UMR 8524 CNRS, UFR de Mathématiques, Université de Lille 1, F-59655 Villeneuve d'Ascq Cédex, France
Address at time of publication:
Département de Mathématiques, Université de Cergy-Pontoise, Site de Saint-Martin, 2 avenue Adolphe Chauvin, 95302 Cergy-Pontoise cedex, France
Email:
germinet@agat.univ-lille1.fr, germinet@math.u-cergy.fr
Abel
Klein
Affiliation:
Department of Mathematics, University of California Irvine, Irvine, California 92697-3875
Email:
aklein@uci.edu
DOI:
10.1090/S0002-9939-04-07431-3
PII:
S 0002-9939(04)07431-3
Keywords:
Schr\"odinger operator,
acoustic operator,
Maxwell operator,
Combes-Thomas estimate,
operator kernel,
Gevrey class
Received by editor(s):
February 13, 2003
Received by editor(s) in revised form:
July 7, 2003
Posted:
April 21, 2004
Additional Notes:
The third author was supported in part by NSF Grant DMS-0200710.
Communicated by:
Joseph A. Ball
Copyright of article:
Copyright
2004,
American Mathematical Society
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