no. 4
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. 
@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://www.numdam.org/item/AIHPA_1999__70_4_381_0/}
}
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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://www.numdam.org/item/AIHPA_1999__70_4_381_0/

[1] S. Agmon, Lectures on exponential decay of solutions of second-order elliptic equations, Mathematical Notes 29, Princeton University Press, Princeton, NJ, 1982. | MR | Zbl

[2] M. Aizenman, Localization at weak disorder: some elementary bounds, Rev. Math. Phys., Vol. 6, N° 5a, 1994, pp. 1163-1182. | MR | Zbl

[3] J.-M. Barbaroux, thèse, Université de Toulon et du Var 1997.

[4] J.-M. Barbaroux, J.M. Combes and P.D. Hislop, Localization near band edges for random Schrödinger operators, Helv. Phys. Acta, Vol. 70, 1997, pp. 16-43. | MR | Zbl

[5] J.-M. Barbaroux, J.M. Combes and P.D. Hislop, Landau Hamiltonians with unbounded random potentials, Lett. Math. Phys., Vol. 40, 1997. | MR | Zbl

[6] D. Belitz and T.R. Kirkpatrick, the Anderson-Mott Transition, Rev. of Modern Phys., Vol. 66, 1994, p. 261.

[7] M.S. Birman and M.Z. Solomjak, Spectral Theory of Self-Adjoint Operators in Hilbert Space, Dordrecht: D. Reidel Publishing Co, 1987. | MR

[8] J.-M. Combes and P.D. Hislop, Localization for some continuous random Hamiltonians in d-dimensions, J. Funct. Anal., Vol. 124, 1994, pp. 149-180. | MR | Zbl

[9] J.-M. Combes and P.D. Hislop, Localization Properties of Continuous Disordered Systems in d-dimensions, Proc. of "Mathematical Quantum Theory", Vancouver, Canada, 1993. | MR | Zbl

[10] J.-M. Combes, P.D. Hislop and E. Mourre, Spectral Averaging, Perturbation of Singular Spectra, and Localization, Trans. Amer. Math. Soc., Vol. 348, 1996, pp. 4883-4894. | MR | Zbl

[11] J.-M. Combes, P.D. Hislop and E. Mourre, Correlated Wegner Inequalities for Long-range and Correlated Potentials, preprint 1997. 1997.

[12] R. Carmona and J. Lacroix, Spectral theory of random Schrödinger operators, Birkhäuser, Boston, 1990. | MR | Zbl

[13] J.-M. Combes and L. Thomas, Asymptotic behavior of eigenfunctions for multiparticle Schrödinger operators, Commun. Math. Phys., Vol. 34, 1973, pp. 251-276. | MR | Zbl

[14] P.A. Deift and R. Hempel, 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

[15] H.J.S. Dorren and A. Tip, Maxwell's equations for non-smooth media; fractal-shaped and pointlike objects, J. Math. Phys., Vol. 32, 1991, p. 3060. | MR

[16] W. Faris, Localization for a random discrete wave equation, in Random Media, IMA Volume 7, G. Papanicolaou, ed., Springer-Verlag, New York, 1987. | MR | Zbl

[17] W. Faris, A localization principle for multiplicative perturbations, J. Funct. Anal., Vol. 67, 1986, pp. 105-114. | MR | Zbl

[18] A. Figotin and A. Klein, Localization phenomenon in gaps of the spectrum of random lattice operators, J. Stat. Phys., Vol. 75, 1994, pp. 997-1021. | MR | Zbl

[19] A. Figotin and A. Klein, Localization of Electromagnetic and Acoustic Waves in Random Media: Lattice Models, J. Stat. Phys., Vol. 76, 1994, pp. 985-1003. | MR | Zbl

[20] A. Figotin and A. Klein, Localization of Classical Waves I: Acoustic Waves, Commun. Math. Phys., Vol. 180, 1996, pp. 439-482. | MR | Zbl

[21] A. Figotin and A. Klein, Localization of Classical Waves II: Electromagnetic Waves, Commun. Math. Phys., Vol. 184, 1997, pp. 411-441. | MR | Zbl

[22] A. Figotin and P. Kuchment, 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

[23] A. Figotin and P. Kuchment, 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

[24] J. Frölich and T. Spencer, 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

[25] F. Gesztesy, 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] J. Howland, Perturbation theory of dense point spectra, J. Funct. Anal., Vol. 74, 1987, pp. 52-80. | MR | Zbl

[27] S. John, The localization of light and other classical waves in disordered media, Comments Cond. Mat. Phys., Vol. 14, 1988, pp. 193-230.

[28] W. Kirsch and F. Martinelli, On the spectrum of Schrödinger operators with a random potential, Commun. Math. Phys., Vol. 85, 1982, pp. 329-350. | MR | Zbl

[29] W. Kirsch, P. Stollnian and G. Stoltz, Localization for random perturbations ofperiodic Schrödinger operators, preprint 1996. | MR

[30] F. Klopp, Internal Lifshits tails for random perturbations of periodic Schrödinger operators, preprint 1997. | MR

[31] S. Kotani and B. Simon, Localization in general one-dimensional systems. II, Commun. Math. Phys., Vol. 112, 1987, pp. 103-120. | MR | Zbl

[32] P. Kuchment, Floquet Theory for Partial Differential Equations, Basel: Birkhäuser Verlag 1993. | MR | Zbl

[33] F.H. Lin, A uniqueness equation for parabolic equations, Comm. Pure Appl. Math., Vol. 43, 1990, pp. 127-136. | Zbl

[34] L. Pastur and A. Figotin, Spectra of random and almost-periodic operators, Berlin: Springer-Verlag 1992. | MR | Zbl

[35] B. Simon, Trace ideals and their applications, Cambridge: Cambridge University Press 1979. | MR | Zbl

[36] B. Sinion and T. Wolff, Singular continuous spectrum under rank one perturbation and localization for random Hamiltonians, Comm. Pure Appl. Math., Vol. 39, 1986, pp. 75-90. | MR | Zbl

[37] T. Spencer, Localization for random and quasi-periodic potentials, J. Stat. Phys., Vol. 51, 1988, pp. 1009-1019. | MR | Zbl

[38] P. Stollmann, Localization for random perturbations of anisotropic periodic media, to appear in Israel Journal of Mathematics 1997. | MR | Zbl

[39] D.V. Van Coevorden, R. Sprik, A. Tip and A. Lagendijk, Photonic Bandstructure of Atomic Lattices, Phys. Rev. Letters, Vol. 77, 1996, p. 2412.

[40] H. Von Dreifus and A. Klein, A new proof of localization in the Anderson tight binding model, Commun. Math. Phys., Vol. 124, 1989, pp. 285-299. | MR | Zbl