@article{AIHPA_1999__70_4_381_0, author = {Combes, J. M. and Hislop, P. D. and Tip, A.}, title = {Band edge localization and the density of states for acoustic and electromagnetic waves in random media}, journal = {Annales de l'I.H.P. Physique th\'eorique}, pages = {381--428}, publisher = {Gauthier-Villars}, volume = {70}, number = {4}, year = {1999}, mrnumber = {1686427}, zbl = {0931.76085}, language = {en}, url = {http://archive.numdam.org/item/AIHPA_1999__70_4_381_0/} }
TY - JOUR AU - Combes, J. M. AU - Hislop, P. D. AU - Tip, A. TI - Band edge localization and the density of states for acoustic and electromagnetic waves in random media JO - Annales de l'I.H.P. Physique théorique PY - 1999 SP - 381 EP - 428 VL - 70 IS - 4 PB - Gauthier-Villars UR - http://archive.numdam.org/item/AIHPA_1999__70_4_381_0/ LA - en ID - AIHPA_1999__70_4_381_0 ER -
%0 Journal Article %A Combes, J. M. %A Hislop, P. D. %A Tip, A. %T Band edge localization and the density of states for acoustic and electromagnetic waves in random media %J Annales de l'I.H.P. Physique théorique %D 1999 %P 381-428 %V 70 %N 4 %I Gauthier-Villars %U http://archive.numdam.org/item/AIHPA_1999__70_4_381_0/ %G en %F AIHPA_1999__70_4_381_0
Combes, J. M.; Hislop, P. D.; Tip, A. Band edge localization and the density of states for acoustic and electromagnetic waves in random media. Annales de l'I.H.P. Physique théorique, Tome 70 (1999) no. 4, pp. 381-428. http://archive.numdam.org/item/AIHPA_1999__70_4_381_0/
[1] Lectures on exponential decay of solutions of second-order elliptic equations, Mathematical Notes 29, Princeton University Press, Princeton, NJ, 1982. | MR | Zbl
,[2] Localization at weak disorder: some elementary bounds, Rev. Math. Phys., Vol. 6, N° 5a, 1994, pp. 1163-1182. | MR | Zbl
,[3] thèse, Université de Toulon et du Var 1997.
,[4] Localization near band edges for random Schrödinger operators, Helv. Phys. Acta, Vol. 70, 1997, pp. 16-43. | MR | Zbl
, and ,[5] Landau Hamiltonians with unbounded random potentials, Lett. Math. Phys., Vol. 40, 1997. | MR | Zbl
, and ,[6] the Anderson-Mott Transition, Rev. of Modern Phys., Vol. 66, 1994, p. 261.
and ,[7] Spectral Theory of Self-Adjoint Operators in Hilbert Space, Dordrecht: D. Reidel Publishing Co, 1987. | MR
and ,[8] Localization for some continuous random Hamiltonians in d-dimensions, J. Funct. Anal., Vol. 124, 1994, pp. 149-180. | MR | Zbl
and ,[9] Localization Properties of Continuous Disordered Systems in d-dimensions, Proc. of "Mathematical Quantum Theory", Vancouver, Canada, 1993. | MR | Zbl
and ,[10] Spectral Averaging, Perturbation of Singular Spectra, and Localization, Trans. Amer. Math. Soc., Vol. 348, 1996, pp. 4883-4894. | MR | Zbl
, and ,[11] Correlated Wegner Inequalities for Long-range and Correlated Potentials, preprint 1997. 1997.
, and ,[12] Spectral theory of random Schrödinger operators, Birkhäuser, Boston, 1990. | MR | Zbl
and ,[13] Asymptotic behavior of eigenfunctions for multiparticle Schrödinger operators, Commun. Math. Phys., Vol. 34, 1973, pp. 251-276. | MR | Zbl
and ,[14] On the existence of eigenvalues of the Schrödinger operator H + λW in a gap of σ(H), Commun. Math. Phys., Vol. 103, 1986, pp. 461-490. | MR | Zbl
and ,[15] Maxwell's equations for non-smooth media; fractal-shaped and pointlike objects, J. Math. Phys., Vol. 32, 1991, p. 3060. | MR
and ,[16] Localization for a random discrete wave equation, in Random Media, IMA Volume 7, G. Papanicolaou, ed., Springer-Verlag, New York, 1987. | MR | Zbl
,[17] A localization principle for multiplicative perturbations, J. Funct. Anal., Vol. 67, 1986, pp. 105-114. | MR | Zbl
,[18] Localization phenomenon in gaps of the spectrum of random lattice operators, J. Stat. Phys., Vol. 75, 1994, pp. 997-1021. | MR | Zbl
and ,[19] Localization of Electromagnetic and Acoustic Waves in Random Media: Lattice Models, J. Stat. Phys., Vol. 76, 1994, pp. 985-1003. | MR | Zbl
and ,[20] Localization of Classical Waves I: Acoustic Waves, Commun. Math. Phys., Vol. 180, 1996, pp. 439-482. | MR | Zbl
and ,[21] Localization of Classical Waves II: Electromagnetic Waves, Commun. Math. Phys., Vol. 184, 1997, pp. 411-441. | MR | Zbl
and ,[22] Band-Gap structure of spectra of periodic dielectric and acoustic media. I. scalar Model, SIAM J. Appl. Math., Vol. 56, No. 1, 1996, pp. 68-88. | MR | Zbl
and ,[23] Band-Gap structure of spectra of periodic dielectric and acoustic media. II. 2D Photonic Crystals, SIAM J. Appl. Math., Vol. 56, No. 6, 1996, pp. 1561-1620. | MR | Zbl
and ,[24] Absence of diffusion in the Anderson tight binding model for large disorder or low energy, Commun. Math. Phys., Vol. 88, 1983, pp. 151-184. | MR | Zbl
and ,[25] Some applications of commutation methods, in Schrödinger operators: Proc. of the Nordic Summer School in Mathematics held at Sandbjerg Slot, Sonderborg, Denmark, 1988, Lecture Notes in Physics No. 345, H. Holden and A. Jensen, eds., Berlin: Springer-Verlag 1989. | MR | Zbl
,[26] Perturbation theory of dense point spectra, J. Funct. Anal., Vol. 74, 1987, pp. 52-80. | MR | Zbl
,[27] The localization of light and other classical waves in disordered media, Comments Cond. Mat. Phys., Vol. 14, 1988, pp. 193-230.
,[28] On the spectrum of Schrödinger operators with a random potential, Commun. Math. Phys., Vol. 85, 1982, pp. 329-350. | MR | Zbl
and ,[29] Localization for random perturbations ofperiodic Schrödinger operators, preprint 1996. | MR
, and ,[30] Internal Lifshits tails for random perturbations of periodic Schrödinger operators, preprint 1997. | MR
,[31] Localization in general one-dimensional systems. II, Commun. Math. Phys., Vol. 112, 1987, pp. 103-120. | MR | Zbl
and ,[32] Floquet Theory for Partial Differential Equations, Basel: Birkhäuser Verlag 1993. | MR | Zbl
,[33] A uniqueness equation for parabolic equations, Comm. Pure Appl. Math., Vol. 43, 1990, pp. 127-136. | Zbl
,[34] Spectra of random and almost-periodic operators, Berlin: Springer-Verlag 1992. | MR | Zbl
and ,[35] Trace ideals and their applications, Cambridge: Cambridge University Press 1979. | MR | Zbl
,[36] Singular continuous spectrum under rank one perturbation and localization for random Hamiltonians, Comm. Pure Appl. Math., Vol. 39, 1986, pp. 75-90. | MR | Zbl
and ,[37] Localization for random and quasi-periodic potentials, J. Stat. Phys., Vol. 51, 1988, pp. 1009-1019. | MR | Zbl
,[38] Localization for random perturbations of anisotropic periodic media, to appear in Israel Journal of Mathematics 1997. | MR | Zbl
,[39] Photonic Bandstructure of Atomic Lattices, Phys. Rev. Letters, Vol. 77, 1996, p. 2412.
, , and ,[40] A new proof of localization in the Anderson tight binding model, Commun. Math. Phys., Vol. 124, 1989, pp. 285-299. | MR | Zbl
and ,