The wave equation in random domains : localization of the normal modes in the small frequency region

Fabio Martinelli

Annales de l'I.H.P. Physique théorique (1985)

  • Volume: 43, Issue: 2, page 227-249
  • ISSN: 0246-0211

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Martinelli, Fabio. "The wave equation in random domains : localization of the normal modes in the small frequency region." Annales de l'I.H.P. Physique théorique 43.2 (1985): 227-249. <http://eudml.org/doc/76300>.

@article{Martinelli1985,
author = {Martinelli, Fabio},
journal = {Annales de l'I.H.P. Physique théorique},
keywords = {models of wave propagation; Anderson localization; Schrödinger equation},
language = {eng},
number = {2},
pages = {227-249},
publisher = {Gauthier-Villars},
title = {The wave equation in random domains : localization of the normal modes in the small frequency region},
url = {http://eudml.org/doc/76300},
volume = {43},
year = {1985},
}

TY - JOUR
AU - Martinelli, Fabio
TI - The wave equation in random domains : localization of the normal modes in the small frequency region
JO - Annales de l'I.H.P. Physique théorique
PY - 1985
PB - Gauthier-Villars
VL - 43
IS - 2
SP - 227
EP - 249
LA - eng
KW - models of wave propagation; Anderson localization; Schrödinger equation
UR - http://eudml.org/doc/76300
ER -

References

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  1. [1] E. Guazzelli, E. Guyon, B. Souillard, On the localization of shallow water waves by a random bottom. J. Phys. (Paris) Lett., t. 44, 1983. 
  2. [2] P.W. Anderson, Absence of diffusion in certain random systems. Phys. Rev., t. 109, 1958. 
  3. [3] D.J. Thouless, Phys. Repts., t. 13, 1974. 
  4. [4] L. Pastur, Spectral properties of disordered systems in one body approximation. Comm. Math. Phys., t. 75, 1980. Zbl0429.60099MR582507
  5. [5] B. Simon, B. Souillard, Franco-American meeting on the mathematics of random and almost periodic potential, J. Stat. Phys., t. 36, 1984. 
  6. [6] J. Frohlich, F. Martinelli, E. Scoppola, T. Spencer, Constructive proof of localization in the Anderson tight-binding model. Comm. Math. Phys. (in press). Zbl0573.60096
  7. [7] B. Simon, T. Wolff, Singular continuous spectrum under rank one perturbations and localization for random Hamiltonians, Preprint Caltech, 1985. MR820340
  8. [8] F. Delyon, Y. Levy, B. Souillard, Anderson localization for multidimensional systems at large disorder or large energy, Comm. Math. Phys. (to appear). Zbl0576.60053MR806247
  9. [9] J. Frohlich, T. Spencer, Absence of diffusion in the Anderson model tight-binding model for large disorder or low energy, Comm. Math. Phys., t. 88, 1983. Zbl0519.60066MR696803
  10. [10] G. Jona-Lasinio, F. Martinelli, E. Scoppola, Multiple tunnelings in d-dimensions: A quantum particle in a hierarchical potential. Ann. Inst. H. Poincaré, t. 42, n° 1, 1985. Zbl0586.35030MR794366
  11. [11] H. Holden, F. Martinelli, Absence of diffusion near the bottom of the spectrum for a Schrödinger operator on L, Comm. Math. Phys., t. 93, 1984. Zbl0546.60063MR742193
  12. [12] M. Serra, Opérateur de Laplace-Beltrami sur une variété quasi périodique, Université de Provence, Marseille, 1983. 
  13. [13] B. Simon, Schrödinger semigroups. Bull. Amer. Math. Soc., t. 7, 1983. Zbl0524.35002MR670130
  14. [14] W. Kirsch, F. Martinelli, On the ergodic properties of the spectrum of general random operators. J. reine angew. Math., t. 334, 1982. Zbl0476.60058MR667454
  15. [15] W. Kirsch, F. Martinelli, On the spectrum of Schrödinger operators with a random potential, Comm. Math. Phys., t. 85, 1982. Zbl0506.60058MR678150
  16. [16] F. Martinelli, E. Scoppola, A remark on the absence of absolutely continuous spectrum in the Anderson model for large disorder or low energy, Comm. Math. Phys., t. 97, 1985. Zbl0608.60094
  17. [17] F. Wegner, Bounds on the density of states in disordered systems, Z. Phys., t. B. 14, 1981. MR639135
  18. [18] W. Kirsch, F. Martinelli, Large deviations and Lifshitz singularity of the integrated density of states of random Hamiltonians, Comm. Math. Phys., t. 89, 1983. Zbl0517.60071MR707770
  19. [19] M. Reed, B. Simon, Methods of modern mathematical physics IV. Acad. Press, 1980. Zbl0401.47001MR751959

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